{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "68f82fa0-6b1f-4ac5-8389-fdc3fb431fed",
   "metadata": {},
   "source": [
    "# 实验4 基于分类模型的手写字母识别"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a755075-27bb-4b30-ac27-c627537e24c3",
   "metadata": {},
   "source": [
    "### 使用torch库载入MNIST数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b58b8970-1dc0-4387-b5f5-b7c5f194fe8b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image size is (28, 28)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from sklearn import svm\n",
    "from sklearn import tree\n",
    "from sklearn.linear_model import LogisticRegression, LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score, mean_absolute_error\n",
    "from sklearn.metrics import classification_report, confusion_matrix\n",
    "import seaborn as sns\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.multiclass import OneVsRestClassifier\n",
    "from sklearn.multiclass import OneVsOneClassifier\n",
    "from sklearn.metrics import roc_curve, auc\n",
    "\n",
    "import time\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "color_list = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:brown', 'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan']\n",
    "\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "label_size = 18 # Label size\n",
    "ticklabel_size = 14 # Tick label size\n",
    "\n",
    "# Load the MNIST dataset to display\n",
    "imgDisp = torchvision.datasets.MNIST(root='D:/BaiduNetdiskDownload', train=False, download=True)\n",
    "img, label = imgDisp[0]\n",
    "\n",
    "print(f'Image size is {img.size}')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7,7))\n",
    "ax.imshow(img, cmap='gray') # Display image\n",
    "ax.tick_params(axis='both', which='major', labelsize=ticklabel_size) # Set tick label size\n",
    "ax.set_title(f\"Label: {label}\", fontsize=label_size)\n",
    "# plt.savefig(f'exp_character{label}.png', dpi=300) # Make figure clearer\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96bd7e2d-0adf-4ef1-9401-f42e8f2c8a86",
   "metadata": {},
   "source": [
    "### 在读取数据的时候提取样本的特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aebaa60c-cd50-49f2-8e18-538d8cc9ec00",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class 0: Trainset - 5923 (9.87%), Testset - 980 (9.80%)\n",
      "Class 1: Trainset - 6742 (11.24%), Testset - 1135 (11.35%)\n",
      "Class 2: Trainset - 5958 (9.93%), Testset - 1032 (10.32%)\n",
      "Class 3: Trainset - 6131 (10.22%), Testset - 1010 (10.10%)\n",
      "Class 4: Trainset - 5842 (9.74%), Testset - 982 (9.82%)\n",
      "Class 5: Trainset - 5421 (9.04%), Testset - 892 (8.92%)\n",
      "Class 6: Trainset - 5918 (9.86%), Testset - 958 (9.58%)\n",
      "Class 7: Trainset - 6265 (10.44%), Testset - 1028 (10.28%)\n",
      "Class 8: Trainset - 5851 (9.75%), Testset - 974 (9.74%)\n",
      "Class 9: Trainset - 5949 (9.92%), Testset - 1009 (10.09%)\n",
      "Input_size is 112\n"
     ]
    }
   ],
   "source": [
    "class ftrExtract(object):\n",
    "    '''\n",
    "    This class is used to extract features of images\n",
    "    '''\n",
    "    def __call__(self, tensor):\n",
    "        tensor = tensor.squeeze() # Compress redundant demensions\n",
    "\n",
    "        mean_width = tensor.mean(axis=0)\n",
    "        mean_height = tensor.mean(axis=1)\n",
    "\n",
    "        std_width = tensor.std(axis=0)\n",
    "        std_height = tensor.std(axis=1)\n",
    "\n",
    "        ftrs = torch.cat([mean_width, mean_height, std_width, std_height])\n",
    "\n",
    "        return ftrs\n",
    "\n",
    "# Define a transform to normalize the data\n",
    "transform = transforms.Compose([transforms.ToTensor(), ftrExtract()])\n",
    "\n",
    "# Load the MNIST dataset\n",
    "trainset = torchvision.datasets.MNIST(root='D:/BaiduNetdiskDownload', train=True, download=True, transform=transform)\n",
    "testset = torchvision.datasets.MNIST(root='D:/BaiduNetdiskDownload', train=False, download=True, transform=transform)\n",
    "\n",
    "# Count number of each class in trainset\n",
    "train_class_counts = {}\n",
    "for _, label in trainset:\n",
    "    if label not in train_class_counts:\n",
    "        train_class_counts[label] = 0\n",
    "    train_class_counts[label] += 1\n",
    "\n",
    "# Count number of each class in testset\n",
    "test_class_counts = {}\n",
    "for _, label in testset:\n",
    "    if label not in test_class_counts:\n",
    "        test_class_counts[label] = 0\n",
    "    test_class_counts[label] += 1\n",
    "\n",
    "# Print results\n",
    "for i in range(10):\n",
    "    cls_counts_train = train_class_counts.get(i, 0)\n",
    "    cls_ratio_train = cls_counts_train / len(trainset)\n",
    "    cls_counts_test = test_class_counts.get(i, 0)\n",
    "    cls_ratio_test = cls_counts_test / len(testset)\n",
    "\n",
    "    print(f\"Class {i}: Trainset - {cls_counts_train} ({cls_ratio_train:.2%}), Testset - {cls_counts_test} ({cls_ratio_test:.2%})\")\n",
    "\n",
    "batch_size = 42\n",
    "trainloader = torch.utils.data.DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=0)\n",
    "testloader = torch.utils.data.DataLoader(testset, batch_size=batch_size, shuffle=False, num_workers=0)\n",
    "\n",
    "# Get a batch of training data\n",
    "dataiter = iter(trainloader)\n",
    "data, labels = next(dataiter)\n",
    "\n",
    "input_size = data[0].numpy().shape[0]  \n",
    "#数据集类型转换为numpy数组，\n",
    "print(f'Input_size is {input_size}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50872aea-6379-4510-9df9-4d39ce1c09d9",
   "metadata": {},
   "source": [
    "### 使用线性回归识别手写字母"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30d6a0cf-7872-4d4b-9812-a00529988f71",
   "metadata": {},
   "source": [
    "#### 构建逻辑回归模型判断大小数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e4eaec3-9111-403d-9f28-6c2deccc1b1e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapes of X_train and Y_train: (60000, 112) and (60000,)\n",
      "Shapes of X_test and y_test: (10000, 112) and (10000,)\n"
     ]
    }
   ],
   "source": [
    "# Convert data to numpy arrays\n",
    "X_train = []\n",
    "y_train = []\n",
    "for batch_image, batch_label in trainloader:\n",
    "    X_train.append(batch_image.view(-1, input_size).numpy())\n",
    "    y_train.append(batch_label.numpy())\n",
    "\n",
    "X_train = np.vstack(X_train)\n",
    "y_train = np.concatenate(y_train)\n",
    "\n",
    "print(f'Shapes of X_train and Y_train: {X_train.shape} and {y_train.shape}')\n",
    "\n",
    "X_test = []\n",
    "y_test = []\n",
    "for batch_image, batch_label in testloader:\n",
    "    X_test.append(batch_image.view(-1, input_size).numpy())\n",
    "    y_test.append(batch_label.numpy())\n",
    "\n",
    "X_test = np.vstack(X_test)\n",
    "y_test = np.concatenate(y_test)\n",
    "\n",
    "print(f'Shapes of X_test and y_test: {X_test.shape} and {y_test.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b93f2ca2-1a37-4ea2-beb6-7637c6350002",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted classes: [0 1 2 3 4 5 6 7 8 9]\n",
      "Real classes: [0 1 2 3 4 5 6 7 8 9]\n",
      "Accuracy of linear regression model: 0.2435\n"
     ]
    }
   ],
   "source": [
    "# Initialize the linear regression model\n",
    "lr_model = LinearRegression()\n",
    "\n",
    "# Train the model\n",
    "lr_model.fit(X_train, y_train)\n",
    "\n",
    "# Make predictions on the test set\n",
    "y_pred = lr_model.predict(X_test)\n",
    "\n",
    "# Round predictions to nearest integer for classification\n",
    "y_pred_constrained = np.clip(y_pred, 0, np.max(y_test))\n",
    "y_pred_rounded = np.round(y_pred_constrained).astype(int)\n",
    "print(f\"Predicted classes: {np.unique(y_pred_rounded)}\")\n",
    "\n",
    "# Calculate accuracy\n",
    "accuracy = np.mean(y_pred_rounded == y_test)\n",
    "print(f\"Real classes: {np.unique(y_test)}\")\n",
    "print(f\"Accuracy of linear regression model: {accuracy:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4ce0b6fd-7e42-4b72-987d-2a942953ec2c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Real label 0, Predict label 0 (168), Predict label 1 (285), Predict label 2 (299), Predict label 3 (164), Predict label 4 (46), Predict label 5 (12), Predict label 6 (6), Predict label 7 (0), Predict label 8 (0), Predict label 9 (0)\n",
      "Real label 1, Predict label 0 (40), Predict label 1 (333), Predict label 2 (389), Predict label 3 (277), Predict label 4 (78), Predict label 5 (14), Predict label 6 (3), Predict label 7 (0), Predict label 8 (0), Predict label 9 (1)\n",
      "Real label 2, Predict label 0 (20), Predict label 1 (86), Predict label 2 (229), Predict label 3 (368), Predict label 4 (231), Predict label 5 (76), Predict label 6 (18), Predict label 7 (4), Predict label 8 (0), Predict label 9 (0)\n",
      "Real label 3, Predict label 0 (0), Predict label 1 (10), Predict label 2 (90), Predict label 3 (264), Predict label 4 (344), Predict label 5 (198), Predict label 6 (82), Predict label 7 (15), Predict label 8 (6), Predict label 9 (1)\n",
      "Real label 4, Predict label 0 (3), Predict label 1 (3), Predict label 2 (24), Predict label 3 (119), Predict label 4 (289), Predict label 5 (247), Predict label 6 (116), Predict label 7 (96), Predict label 8 (63), Predict label 9 (22)\n",
      "Real label 5, Predict label 0 (0), Predict label 1 (5), Predict label 2 (26), Predict label 3 (168), Predict label 4 (295), Predict label 5 (236), Predict label 6 (104), Predict label 7 (46), Predict label 8 (12), Predict label 9 (0)\n",
      "Real label 6, Predict label 0 (0), Predict label 1 (9), Predict label 2 (24), Predict label 3 (84), Predict label 4 (153), Predict label 5 (282), Predict label 6 (251), Predict label 7 (113), Predict label 8 (35), Predict label 9 (7)\n",
      "Real label 7, Predict label 0 (0), Predict label 1 (0), Predict label 2 (4), Predict label 3 (14), Predict label 4 (25), Predict label 5 (57), Predict label 6 (224), Predict label 7 (446), Predict label 8 (224), Predict label 9 (34)\n",
      "Real label 8, Predict label 0 (0), Predict label 1 (1), Predict label 2 (7), Predict label 3 (61), Predict label 4 (219), Predict label 5 (286), Predict label 6 (234), Predict label 7 (107), Predict label 8 (42), Predict label 9 (17)\n",
      "Real label 9, Predict label 0 (1), Predict label 1 (1), Predict label 2 (4), Predict label 3 (12), Predict label 4 (43), Predict label 5 (52), Predict label 6 (58), Predict label 7 (270), Predict label 8 (391), Predict label 9 (177)\n"
     ]
    }
   ],
   "source": [
    "def manual_confusion_matrix(y_true, y_pred, num_classes):\n",
    "    cm = np.zeros((num_classes, num_classes), dtype=int)\n",
    "    for t, p in zip(y_true, y_pred):\n",
    "        cm[t][p] += 1\n",
    "    return cm\n",
    "\n",
    "# Get number of character types\n",
    "num_classes = len(np.unique(y_test)) \n",
    "\n",
    "# Calculate confusion matrix\n",
    "cm = manual_confusion_matrix(y_test, y_pred_rounded, num_classes)\n",
    "\n",
    "# Print the results in the specified format\n",
    "for i in range(num_classes):\n",
    "    output = f\"Real label {i}, \"\n",
    "    for j in range(num_classes):\n",
    "        output += f\"Predict label {j} ({cm[i, j]}), \"\n",
    "    print(output[:-2])  # Remove the last comma and space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa9daf7b-5779-4eca-8c89-e8ee8ef9935c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted classes: [0 1 2 3 4 5 6 7 8 9]\n",
      "Accuracy of logistic regression model: 0.8735\n",
      "\n",
      "Classification Report:\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.92      0.95      0.93       980\n",
      "           1       0.93      0.96      0.95      1135\n",
      "           2       0.86      0.84      0.85      1032\n",
      "           3       0.80      0.84      0.82      1010\n",
      "           4       0.91      0.91      0.91       982\n",
      "           5       0.77      0.69      0.73       892\n",
      "           6       0.92      0.92      0.92       958\n",
      "           7       0.91      0.89      0.90      1028\n",
      "           8       0.83      0.83      0.83       974\n",
      "           9       0.86      0.89      0.87      1009\n",
      "\n",
      "    accuracy                           0.87     10000\n",
      "   macro avg       0.87      0.87      0.87     10000\n",
      "weighted avg       0.87      0.87      0.87     10000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initialize the linear regression model\n",
    "lr_model = LogisticRegression(max_iter=1000)\n",
    "\n",
    "# Train the model\n",
    "lr_model.fit(X_train, y_train)\n",
    "\n",
    "# Make predictions on the test set\n",
    "y_pred = lr_model.predict(X_test)\n",
    "y_pred_proba = lr_model.predict_proba(X_test)\n",
    "\n",
    "# Round predictions to nearest integer for classification\n",
    "y_pred_rounded = np.round(y_pred).astype(int)\n",
    "print(f\"Predicted classes: {np.unique(y_pred_rounded)}\")\n",
    "\n",
    "# Calculate accuracy\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "print(f\"Accuracy of logistic regression model: {accuracy:.4f}\")\n",
    "\n",
    "# Calculate and print classification report\n",
    "print(\"\\nClassification Report:\")\n",
    "print(classification_report(y_test, y_pred))\n",
    "\n",
    "cm = confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9e8db62a-6881-4c12-b20a-de37ec6e4bb0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now let's create the confusion matrix plot\n",
    "fig, ax = plt.subplots(figsize=(10, 8))\n",
    "\n",
    "# Plot the confusion matrix as a heatmap\n",
    "im = ax.imshow(cm, interpolation='nearest', cmap=plt.cm.Blues)\n",
    "\n",
    "# Set up the axes\n",
    "ax.set(xticks=np.arange(cm.shape[1]),\n",
    "       yticks=np.arange(cm.shape[0]),\n",
    "       xticklabels=np.arange(10), yticklabels=np.arange(10),\n",
    "       xlabel='Predicted label', ylabel='True label')\n",
    "\n",
    "# Loop over data dimensions and create text annotations\n",
    "for i in range(cm.shape[0]):\n",
    "    for j in range(cm.shape[1]):\n",
    "        ax.text(j, i, format(cm[i, j], 'd'),\n",
    "                ha=\"center\", va=\"center\", fontsize=ticklabel_size,\n",
    "                color=\"white\" if cm[i, j] > cm.max() / 2. else \"black\")\n",
    "\n",
    "# Adjust font sizes\n",
    "ax.set_xlabel('Predicted label', fontsize=label_size)\n",
    "ax.set_ylabel('True label', fontsize=label_size)\n",
    "\n",
    "ax.tick_params(axis='both', which='major', labelsize=ticklabel_size)\n",
    "\n",
    "# Tight layout to ensure everything fits\n",
    "fig.tight_layout()\n",
    "\n",
    "# Save the figure if needed\n",
    "# plt.savefig('Logicregression_for_classification.png', dpi=300, bbox_inches='tight')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c5653780-136e-4184-8ea0-c1c9a26e0db1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted classes:  [1 2 2]\n",
      "Probabilities:\n",
      "Example 1: 0.00%, 99.27%, 0.00%, 0.00%, 0.15%, 0.00%, 0.00%, 0.01%, 0.56%, 0.01%\n",
      "Example 2: 0.01%, 0.00%, 94.84%, 0.00%, 0.08%, 1.54%, 3.02%, 0.00%, 0.50%, 0.01%\n",
      "Example 3: 20.43%, 0.30%, 34.51%, 4.15%, 0.32%, 5.62%, 19.69%, 0.02%, 14.82%, 0.14%\n"
     ]
    }
   ],
   "source": [
    "# Select an example of character 1 randomly\n",
    "# Select an example of 1 randomly\n",
    "char_1_indices = np.where(y_test == 1)[0]\n",
    "random_char_1_index = np.random.choice(char_1_indices)\n",
    "random_char_1 = X_test[random_char_1_index]\n",
    "\n",
    "# Select an example of 2 randomly\n",
    "char_2_indices = np.where(y_test == 2)[0]\n",
    "random_char_2_index = np.random.choice(char_2_indices)\n",
    "random_char_2 = X_test[random_char_2_index]\n",
    "\n",
    "# Select an example of 6 randomly\n",
    "char_6_indices = np.where(y_test == 6)[0]\n",
    "random_char_6_index = np.random.choice(char_6_indices)\n",
    "random_char_6 = X_test[random_char_6_index]\n",
    "\n",
    "# Get predictions and probabilities for these examples\n",
    "examples = [random_char_1, random_char_2, random_char_6]\n",
    "example_predictions = lr_model.predict(examples)\n",
    "example_probabilities = lr_model.predict_proba(examples)\n",
    "\n",
    "print(\"Predicted classes: \", example_predictions)\n",
    "\n",
    "# Display probabilities in percentage style, one line per example\n",
    "print(\"Probabilities:\")\n",
    "for i, probs in enumerate(example_probabilities):\n",
    "    prob_strings = [f\"{prob:.2%}\" for _, prob in enumerate(probs)]\n",
    "    print(f\"Example {i+1}: {', '.join(prob_strings)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b419e43d-fb06-4816-bcb2-869ecd4f7f38",
   "metadata": {},
   "source": [
    "### 构建二分类数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ea4d0dbc-d9c9-42de-ae64-b03d041e3aea",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Extract features and labels from trainset\n",
    "x_train = []\n",
    "y_train = []\n",
    "for image, label in trainset:\n",
    "    x_train.append(image.numpy())\n",
    "    y_train.append(1 if label == 1 else 0)  # Set label to 1 for character 1, 0 otherwise\n",
    "\n",
    "x_train = np.array(x_train)\n",
    "y_train = np.array(y_train)\n",
    "\n",
    "# Extract features and labels from trainset\n",
    "x_test = []\n",
    "y_test = []\n",
    "for image, label in testset:\n",
    "    x_test.append(image.numpy())\n",
    "    y_test.append(1 if label == 1 else 0)  # Set label to 1 for character 1, 0 otherwise\n",
    "\n",
    "x_test = np.array(x_test)\n",
    "y_test = np.array(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "97248d35-062e-460f-9528-e5a0c5cf52bf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate x values\n",
    "x = np.linspace(0.01, 5, 1000)\n",
    "\n",
    "# Compute natural logarithm\n",
    "y = -np.log(x)\n",
    "\n",
    "# Create the plot\n",
    "fig, ax_log = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "ax_log.plot(x, y, label='ln(x)', color='k', linewidth=2)\n",
    "\n",
    "ax_log.set_xlabel('x', fontsize=label_size)\n",
    "ax_log.tick_params(axis='both', which='major', labelsize=ticklabel_size)\n",
    "\n",
    "ax_log.set_xlim(-0.05, 5)\n",
    "ax_log.set_ylim(-2, 4)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('natural_logarithm_function.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1e9cf0c-c4b5-4174-9727-2ae919b358b7",
   "metadata": {},
   "source": [
    "### 训练逻辑回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e8ddc0b1-0b84-47d0-a7d1-2ce8e4847303",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Define linear function\n",
    "def linear(X, w, b):\n",
    "    '''        \n",
    "    Parameters:\n",
    "    X (numpy array): Input features, shape (n_samples, n_features)\n",
    "    w (numpy array): Weight vector, shape (n_features,)\n",
    "    b (float): Bias term\n",
    "    '''\n",
    "    return np.dot(X, w) + b\n",
    "\n",
    "# Define sigmoid function\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "# Define forward function\n",
    "def forward(X, w, b):\n",
    "    '''        \n",
    "    Parameters:\n",
    "    X (numpy array): Input features, shape (n_samples, n_features)\n",
    "    w (numpy array): Weight vector, shape (n_features,)\n",
    "    b (float): Bias term\n",
    "    '''\n",
    "    return sigmoid(linear(X, w, b))\n",
    "\n",
    "# Predict probability function\n",
    "def predict(X, w, b):\n",
    "    y_proba = forward(X, w, b)\n",
    "    y_pred = (y_proba >= 0.5).astype(int)\n",
    "    return y_pred, y_proba\n",
    "\n",
    "# Binary cross-entropy\n",
    "def binary_cross_entropy(y, y_pred, eps=1e-15):\n",
    "    return -(y * np.log(y_pred + eps) + (1 - y) * np.log(1 - y_pred + eps))\n",
    "    \n",
    "# Define compute_loss function\n",
    "def compute_loss(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Compute the binary cross-entropy loss for logistic regression.\n",
    "    \n",
    "    Parameters:\n",
    "    X (numpy array): Input features, shape (n_samples, n_features)\n",
    "    y (numpy array): True labels, shape (n_samples,)\n",
    "    w (numpy array): Weight vector, shape (n_features,)\n",
    "    b (float): Bias term\n",
    "    \n",
    "    Returns:\n",
    "    float: Average binary cross-entropy loss\n",
    "    \"\"\"    \n",
    "    n = X.shape[0] # number of samples\n",
    "    \n",
    "    # Compute model predictions\n",
    "    y_pred = forward(X, w, b)\n",
    "    \n",
    "    # Compute loss\n",
    "    loss = 1/n * np.sum(binary_cross_entropy(y, y_pred))\n",
    "    \n",
    "    return loss\n",
    "\n",
    "# Compute gradients\n",
    "def compute_gradients(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Compute the gradients for logistic regression.\n",
    "    \n",
    "    Parameters:\n",
    "    X (numpy array): Input features, shape (n_samples, n_features)\n",
    "    y (numpy array): True labels, shape (n_samples,)\n",
    "    w (numpy array): Weight vector, shape (n_features,)\n",
    "    b (float): Bias term\n",
    "    \n",
    "    Returns:\n",
    "    dw: gradients of weights\n",
    "    db: gradients of bias\n",
    "    \"\"\"\n",
    "    n = X.shape[0] # number of samples\n",
    "    \n",
    "    # Compute model predictions\n",
    "    y_pred = forward(X, w, b)\n",
    "    \n",
    "    dw = 1/n * np.dot(X.T, (y_pred - y))\n",
    "    db = 1/n * np.sum(y_pred - y)\n",
    "    \n",
    "    return dw, db\n",
    "\n",
    "# Train logistic regression model\n",
    "def train_logistic_regression(X, y, learning_rate=0.01, num_iterations=1000):\n",
    "    \"\"\"\n",
    "    Compute the gradients for logistic regression.\n",
    "    \n",
    "    Parameters:\n",
    "    X (numpy array): Input features, shape (n_samples, n_features)\n",
    "    y (numpy array): True labels, shape (n_samples,)\n",
    "    \n",
    "    Returns:\n",
    "    w: weights of logistic regression model\n",
    "    b: bias of logistic regression model\n",
    "    \"\"\"\n",
    "    eps = 1e-15\n",
    "    _, ftr_num = X.shape\n",
    "    \n",
    "    w = np.zeros(ftr_num)\n",
    "    b = 0.0\n",
    "    \n",
    "    # Initialize Adagrad accumulators\n",
    "    lr_w = np.zeros(ftr_num)\n",
    "    lr_b = 0.0\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        # Compute loss and gradients\n",
    "        loss = compute_loss(X, y, w, b)\n",
    "        dw, db = compute_gradients(X, y, w, b)\n",
    "        \n",
    "        # Update accumulators\n",
    "        lr_w = dw ** 2\n",
    "        lr_b = db ** 2\n",
    "        \n",
    "        # Update parameters\n",
    "        w -= learning_rate / (np.sqrt(lr_w) + eps) * dw\n",
    "        b -= learning_rate / (np.sqrt(lr_b) + eps) * db\n",
    "        \n",
    "        # Print loss every 100 iterations\n",
    "        if i % 100 == 0:\n",
    "            print(f\"Iteration {i}, Loss: {loss}\")\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "de606d23-c22e-4ad3-9e66-4ec8d16d5364",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0, Loss: 0.6931471805599435\n",
      "Iteration 100, Loss: 0.12422293332655861\n",
      "Iteration 200, Loss: 0.10062522295557218\n",
      "Iteration 300, Loss: 0.09299181897738767\n",
      "Iteration 400, Loss: 0.08809407647531457\n",
      "Iteration 500, Loss: 0.08451829392045176\n",
      "Iteration 600, Loss: 0.0825571422250939\n",
      "Iteration 700, Loss: 0.08106430367062357\n",
      "Iteration 800, Loss: 0.08001654373457909\n",
      "Iteration 900, Loss: 0.07926216748886451\n",
      "Precision: 0.9287, Recall: 0.8493, Accuracy: 0.9755, F1-Score: 0.8873\n"
     ]
    }
   ],
   "source": [
    "# Train the model\n",
    "w, b = train_logistic_regression(x_train, y_train)\n",
    "\n",
    "y_pred, y_proba = predict(x_test, w, b)\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "precision = precision_score(y_test, y_pred)\n",
    "recall = recall_score(y_test, y_pred)\n",
    "f1 = f1_score(y_test, y_pred)\n",
    "\n",
    "print(f'Precision: {precision:.4f}, Recall: {recall:.4f}, Accuracy: {accuracy:.4f}, F1-Score: {f1:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ddfb50bb-8209-4ee9-bb23-8fd20c8f6192",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 1: imgDisp label is 1, x label is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 2: imgDisp label is 6, x label is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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s6h/zsufe+zxe7nlv06ZNtUPU4cOHJUmJiYnV2u9KlX1tVva42rRpI0k6f/68Tpw4ETDUV9SzVzZknzt3zrapAXmPebn3iHd9RW2sqfpO7H/ixAmr/cv+u7L9y/4fV93zg9AjRCHojh8/rlGjRqmkpER33nmnpk+fru7du6thw4a+bd5///1KP5lLdp/gvNMeNGzYMGjhqKrK/hH1DpQN5Ac/+IHv3/v27auREJWQkGD19Y6kCr/KKzvlxObNm63bXZOf3OtCr0BtaqO3lys/P1+nTp2q8Gsrb6gt2ytWnfqXC8UV1W/durW2b99+RfufOHGi0v1PnTrluwRT2f1jYmIUExOjoqKiSvcvu6665wehx5goBN0777wjj8ej+Ph4/fWvf1VKSopfgJL+3TNQmcq+6pP+/Z9T2Z6Rli1bSro4PqQq17wKpqZNm/qCVGV/KE2ZOZRq0x/Uyynbe/LZZ59Ve3/v81jV5706WrVqJUnWwdFW2ddmZY/Luy4iIkLx8fE13q6qquovy7y/cqvsF3yV1f/+++919OjRgNtcuHBBX331VcD63v2//PLLCueNK1u7ov3L/grxUpX9QtF723Z/1H6EKATdgQMHJEkdO3as8JPre++9V6U6e/bsCbiuqKhI//rXvyRdHEPj1aNHD1/wWLlyZbXaHQz9+vWTdPE/fVPBhJNffvml79833HBDUNrlhPj4eN10002S7M6993nctm1bhQNwc3JyLhuyAunRo4ck6R//+IfOnDlT5f3KDuSu6PmqzK233uqr8f7771e4nff9cPPNNwccDxUqvXr18n0AevfddwNus2/fPt9r1vv6rqrU1FTfvyuqv2nTJt/r4dL63v2Liop8494uVbZu2eOVvf3ll19q//79le7fsGFD9erVK+D+H330UYU93979ExMT1bFjx4DboPYiRCHo4uLiJEnffPNNwD9YO3bs0KuvvlqlWs8880zA+3/3u9/p9OnTioiI8P2ySbr4yd/7a6Xf/va3+uabbyqtH+yBuKNHj5Z0MSC+/vrr5daXlpZqwYIFki5+/XfrrbcGtX1X6mc/+5mki4HhckHq0nM/ePBgRURE6PTp0/rd734XcJ/KBqtXZtSoUQoPD9fx48c1Y8aMKu9XdoC79yud6mjSpIlvBvjf/va3Af/Q7ty50/cL0/T09GofoyZFR0dr8ODBkqT/+Z//UWFhYblt5s2bJ+ni11tpaWnVqt+2bVtfMPnd734XcEzXc889J+liCLn99tv91qWkpPjGuXm3K+vcuXO+11KvXr3Utm1bv/UDBw5UTEyMjDEB9y8oKNCiRYskXXx9RkdH+60fPny4wsPDVVRUpIULF5bbPzc31/c+GDFiRIAzgFovdLMroD4oOy/S0aNHK12819X65ptvfHPyDBo0yDeTcklJiXn99dfNtddea6655poK59/xHtM7y/WvfvUrc/ToUWPMxblZnn32WV/9Rx55pNz+e/bs8dW/9tprzdKlS01BQYFv/dGjR80bb7xhBg4caPr161duf2+7amLGcmP+PY9VkyZNzMqVK33XC9u/f79vBmVJJjMzs9y+ZecNCjQr9+VUZcbyQKo6X9KZM2d8s5VHRESYp556yuzfv9+3vri42GzYsME8/PDDpkmTJuX2984oHhYWZn7zm9/45pr6/vvvfXOLeV8X1Z2x3Du7tf7//GTffPONb933339vVq5cadLS0vz2KS4uNpGRkUaSmT9/viktLQ34uCubJ2r79u2+Gd579epldu3aZYwx5sKFC+btt982rVu3NpJMu3btfBe/9arqea/sNXsl80QZ438B4t69e/vO28mTJ82sWbN8s8lXdAHiyx2/7AWIy/5/cfz4cd/FfaWqXYD4oYceMsePHzfGGHPw4EHfPFRVuQCxy+Uys2bNMidPnjTGXJxbzHtdv6pcgDgyMtL84Q9/8M3Ev23bNnPTTTcZ6eJ1B8v+H4S6gxCFK3Lp5VsqW8pOzvjEE0/4rYuLi/P9IbnhhhvMn/70p8uGqLKXfQkLCzNNmzb1/WcryfTt29ecPn06YLu3b99ukpKSfNt6LxvjvWxG2RqXqukQdfLkSXP77bf76rjdbr/Li0gy06dPD7hvbQ9RxlwMqXfeeaff44mNjfW7fIs3ZF3q9OnTpm/fvr5twsPDTXx8vGOXffEGMe/SuHHjCi/74jV27Fjf+kaNGpnrr7/eJCYm+k28eLnLvqxcudIXxrznIyoqyne7Kpd9qUxNhihjjHn77bfLnaey78VRo0ZVGDCrcvzFixf7Xcbm0tfK5S42XfZ96XK5/CavjYiIMIsXL65w39LSUjN69Gi/11zZyxQ1atTIvP322xXuf+mliho0aOB3ialrrrnGbNu2rdL2o/bi6zyExHPPPaf/+7//8/0q79y5c2rfvr2mTp2qTz/9tMq/Upk3b55Wrlypnj17qrS0VJGRkUpOTtaLL76od999t8I5f2655RZ98cUXWrhwofr27atmzZr55qnq0KGDHnzwQa1cudLvsh7BEh0drQ0bNmjx4sW6/fbbFR0drZMnT+q6667T0KFDtWnTpgonhPQOqg4LC9MPf/jDYDa7ypo1a6b33ntPb775pu6//34lJCSopKREp0+f1nXXXad77rlHCxcuDDjIOyoqSuvWrdOLL76o5ORkRUZGyhij3r17a9WqVQG/cqmq8PBwLVy4UNnZ2Ro2bJiuv/56nTt3TpGRkercubPGjh3rN3Gr13//939r5syZvkHI+/fv1759+3Ts2LEqH3vIkCH6/PPPNX78eLVr104lJSWKiIhQcnKyZs2apd27d/v9KrO2uffee7Vr1y6NGzdOSUlJOn36tJo0aaLU1FStXr1ay5Ytu6IfQWRkZGjLli168MEHdd111+nUqVNq3ry50tLS9P777192ktWZM2fq/fffV1pampo3b65Tp07puuuu813sPCMjo8J9XS6XXn75Za1evVqpqamKj4/XmTNnlJiYqHHjxmnnzp269957K9zf7XZr3bp1Wrx4sXr16qXo6GidO3dOHTp00MSJE/X5559XOmUIajeXMRajIQHUShkZGVq6dKmGDx/OVeEBoIYRooB6pG3btjp48KC++uqrcoNkAQDO4us8oJ7Yt2+fvvvuO40dO5YABQBBQE8UAACABXqiAAAALBCiAAAALBCiAAAALESEugHVUVpaqkOHDikmJqZOXXgVAADUDcYYFRUVqXXr1n7XxwykToWoQ4cOKSEhIdTNAAAA9dyBAwfUpk2bSrepU1/nxcTEhLoJAADgKlCVzFGnQhRf4QEAgGCoSuYIWoj65JNPdO+99yo+Pl7R0dHq3r27Xn311WAdHgAAwFFBGROVlZWl/v37KzIyUkOHDlVcXJzWrFmjYcOGKTc3V1OnTg1GMwAAABxT4zOWnz9/Xp06ddLBgwf18ccf65ZbbpEkFRUV6b/+67/09ddf64svvlCHDh0uW8vj8SguLq4mmwsAAKDCwkLFxsZWuk2Nf533wQcfaM+ePXrwwQd9AUq6OGDr6aef1vnz57Vs2bKabgYAAICjajxEZWVlSZL69etXbp33vg8//LCmmwEAAOCoGg9ROTk5khTw67r4+Hg1a9bMtw0AAEBdUeMDywsLCyWpwrFMsbGxOnjwYMB1JSUlKikp8d32eDzONxAAAMBCrZ4nau7cuYqLi/MtzFYOAABqixoPUd4eKG+P1KUq+8XdlClTVFhY6FsOHDhQY+0EAACojhoPUd6xUIHGPeXn5+vYsWMVTm/gdrsVGxvrtwAAANQGNR6iUlJSJEnr168vt857n3cbAACAuiIok2127NhReXl52rx5s5KTkyX5T7b5+eef68Ybb7xsLSbbBAAAwVCVyTZr/Nd5ERERWrJkifr376/evXsrPT1dsbGxWrNmjb777jvNmTOnSgEKAACgNqnxniivrVu3asaMGfr444919uxZde7cWY8++qiGDRtW5Rr0RAEAgGCoSk9U0EKUEwhRAAAgGGrFtfMAAADqI0IUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACAhYhQNwAAapLL5XK0Xt++fR2rNXDgQMdqjR8/3rFaYWHOfr7evHmzY7UyMjIcq/X55587VgtXJ3qiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALESEugEAcKnbb7/dsVpPPvmkY7UkqX///o7Wq41KS0sdrdegQQPHaoWHhztWC7hS9EQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYiAh1AwDUDwMHDnSs1rPPPutYrY4dOzpWS5JKSkocq/WPf/zDsVpOnrPdu3c7VkuSzp07VytrAVeKnigAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALhCgAAAALEaFuAIDQGTp0qGO1Xn75Zcdqud1ux2qtXbvWsVqSNHfuXMdqbdu2zbFaAIKPnigAAAALhCgAAAALhCgAAAALQQlRSUlJcrlcAZcJEyYEowkAAACOCtrA8ri4OD366KPl7u/WrVuwmgAAAOCYoIWoJk2aaObMmcE6HAAAQI1iTBQAAICFoPVElZSUaPny5crLy1N8fLx69Oihm2++OViHBwAAcFTQQtThw4c1atQov/vuvvtuvfLKK2rWrFnAfUpKSlRSUuK77fF4arKJAAAAVRaUr/PGjBmjrKwsHT16VB6PR5s3b9Y999yjd999VwMGDJAxJuB+c+fOVVxcnG9JSEgIRnMBAAAuKyghavr06UpJSVGzZs0UExOj2267TX/729/Uq1cvffzxx3rnnXcC7jdlyhQVFhb6lgMHDgSjuQAAAJcVsoHlYWFhGj16tCRp06ZNAbdxu92KjY31WwAAAGqDkP46zzsW6tSpU6FsBgAAQLWFNERt2bJF0sUZzQEAAOqSGg9RX3zxhQoKCsrdn52drQULFsjtdmvQoEE13QwAAABH1fgUB6tWrdL8+fN11113KSkpSW63W7t379b69esVFhamRYsW6frrr6/pZgAAADiqxkNUnz599OWXX2r79u368MMPdebMGbVo0UJDhgzRxIkT1b1795puAgAAgONqPESlpKQoJSWlpg8DAAAQVC5T0UyXtZDH41FcXFyomwGETLt27Rytt3v3bsdqRUZGOlbriy++cKzWPffc41gtSTp48KCj9QDUToWFhZedWokLEAMAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFiICHUDAFTda6+95mi9yMhIx2qdP3/esVq/+MUvHKt18OBBx2oBQFn0RAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFggRAEAAFiICHUDgPouLS3NsVq33HKLY7WcNmHCBMdqffjhh47VAoCaQk8UAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACAhYhQNwCojRo2bOhYraeeesqxWmFhzn7uyc/Pd6zWO++841gtAKgL6IkCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwQIgCAACwEBHqBgC10WOPPeZYrVtvvdWxWsXFxY7VkqS0tDTHah05csSxWgBQF9ATBQAAYIEQBQAAYIEQBQAAYKHaIWrFihUaP368unXrJrfbLZfLpczMzAq393g8mjRpkhITE+V2u5WYmKhJkybJ4/FcSbsBAABCqtoDy6dNm6Z9+/apWbNmatWqlfbt21fhtsXFxUpJSdGOHTuUmpqq9PR07dy5U88//7w2bNig7OxsRUdHX9EDAAAACIVq90QtWbJEubm5Onr0qCZMmFDptvPnz9eOHTs0efJkrV+/Xs8995zWrVun6dOna8eOHZo/f751wwEAAEKp2iGqb9++SkxMvOx2xhgtWbJEjRs31vTp0/3WTZkyRfHx8Vq6dKmMMdVtAgAAQMjV2MDynJwcHTp0SD179iz3lV1UVJRuv/125eXl6dtvv62pJgAAANSYGg1RktShQ4eA6733e7cLpKSkRB6Px28BAACoDWosRBUWFkqS4uLiAq6PjY312y6QuXPnKi4uzrckJCQ431AAAAALtXqeqClTpqiwsNC3HDhwINRNAgAAkFSD187z9kBV1NPk/Wquop4qSXK73XK73c43DgAA4ArVWE/U5cY8XW7MFAAAQG1WoyGqdevW2rRpU7krz585c0YbN25U69at1b59+5pqAgAAQI2psRDlcrmUkZGhkydPavbs2X7r5s6dq/z8fGVkZMjlctVUEwAAAGpMtcdELVmyRNnZ2ZKkzz77zHdfVlaWJCktLU1paWmSpMmTJ+utt97S/Pnz9emnn6pr167auXOn1q1bp+TkZE2ePNmZRwEAABBk1Q5R2dnZWr58ud99mzZt0qZNmyRJSUlJvhAVHR2trKwszZo1S6tXr1ZWVpZatmypiRMnasaMGVw3DwAA1FnVDlGZmZnKzMys8vZxcXFasGCBFixYUN1DAQAA1Fq1ep4oAACA2qrG5okC6jLvV9K1jdPXmvSObwQAVB89UQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYIUQAAABYiQt0AwCk/+tGPHKuVnJzsWC0nrVmzJtRNAAD8f/REAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWIgIdQMAp1xzzTWO1XK5XI7VctIf//jHUDcBDmrbtq1jtVq1auVYrQceeMCxWpI0ZswYx2pFRkY6VuvMmTOO1Ro2bJhjtSRp/fr1jtU6e/asY7Xgj54oAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAACxGhbgDglHbt2oW6CTWutLQ01E2oczp27OhovYkTJzpWKz093bFajRs3dqzW1cLJc/bmm286VkuS/vd//9exWj//+c8dqwV/9EQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYIEQBAABYiAh1AwCnHDhwINRNqHGNGzd2tN6xY8ccqxUW5txnsmnTpjlW64knnnCsliRFRUU5VuvkyZOO1dqxY4djtVatWuVYLUn685//7Fitm266ybFaP/zhDx2r5eRrVpLGjh3rWK0lS5Y4Vmv79u2O1aoP6IkCAACwQIgCAACwUO0QtWLFCo0fP17dunWT2+2Wy+VSZmZmwG1nzpwpl8sVcHGySxwAACDYqj0matq0adq3b5+aNWumVq1aad++fZfdZ+TIkUpKSvI/cATDsQAAQN1V7SSzZMkSdejQQYmJiXruuec0ZcqUy+4zatQo3XHHHTbtAwAAqJWqHaL69u1bE+0AAACoU4LyndpHH32krVu3Kjw8XJ06dVLfvn3ldruDcWgAAIAaEZQQNX36dL/brVq10vLly5WamhqMwwMAADiuRqc4SE5O1vLly5Wbm6vTp08rJydHzzzzjAoKCjRgwADt3Lmz0v1LSkrk8Xj8FgAAgNqgRkNUWlqafvrTnyoxMVFRUVFq3769pk2bphdffFFnzpzRnDlzKt1/7ty5iouL8y0JCQk12VwAAIAqC8lkmyNHjlRERIQ2bdpU6XZTpkxRYWGhb7kaLusBAADqhpBM1hQZGamYmBidOnWq0u3cbjcD0AEAQK0Ukp6onJwc5efnl5uAEwAAoK6osRBVVFSkXbt2lbs/Pz/fd3Xq9PT0mjo8AABAjbKasTw7O1uS9Nlnn/nuy8rKknRxMHlaWpqOHz+um2++Wd26dVOXLl3UvHlz5eXlad26dTp+/LhSU1M1ceJE5x4JAABAEFU7RGVnZ2v58uV+923atMk3SDwpKUlpaWlq2rSpHn74YW3evFl//etfVVBQoOjoaHXp0kXDhw9XRkaGwsPDnXkUAAAAQVbtEJWZmanMzMzLbhcbG6uFCxfatAkAAKDWC8nAcgAAgLouJFMcADVh3bp1jtU6e/asY7UiIyMdqzV8+HDHakm67IS31TFlyhTHas2YMcOxWsYYx2pJ0tKlSx2r9fvf/96xWrt373asVm22d+9ex2pt2bLFsVrTpk1zrJYkRUQ49+e5c+fOjtXavn27Y7XqA3qiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALBCiAAAALESEugGAU/Ly8hyrtXXrVsdq9erVy7FaP//5zx2rJUn33HOPY7V++MMfOlarqKjIsVqPP/64Y7UkafHixY7WQ+g0bNgw1E0IipKSklA3od6iJwoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMBCRKgbANRGr732mmO1Onfu7FitFi1aOFarJuo5ZcKECY7VWrlypWO1YKdhw4aO1Ro2bJhjtR555BHHajlt4cKFjtVatWqVY7Xgj54oAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAAC4QoAAAACy5jjAl1I6rK4/EoLi4u1M0AqmXevHmO1fr1r3/tWK3a7MiRI47VWrp0qWO1JKmgoMDRerXRgAEDHK2XkJDgWK3ExETHajnpm2++cbRe7969Hat17Ngxx2pdTQoLCxUbG1vpNvREAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWCBEAQAAWHAZY0yoG1FVHo9HcXFxoW4GEDIvvPCCo/V++ctfOloPqGn5+fmO1Vq6dKljtZ544gnHaqF2KCwsVGxsbKXb0BMFAABggRAFAABgoVohKi8vTy+88IL69eun66+/XpGRkWrZsqUGDx6sLVu2BNzH4/Fo0qRJSkxMlNvtVmJioiZNmiSPx+PIAwAAAAiFaoWol156SRMnTtTevXuVmpqqxx57TL169dKbb76pHj16aNWqVX7bFxcXKyUlRc8//7w6duyoiRMn6qabbtLzzz+vlJQUFRcXO/pgAAAAgiWiOht3795dGzduVO/evf3u/+ijj3TXXXfpoYce0n333Se32y1Jmj9/vnbs2KHJkydr3rx5vu1nzJih2bNna/78+Zo1a5YDDwMAACC4qtUTNWjQoHIBSpJ69+6tPn366MSJE/rss88kScYYLVmyRI0bN9b06dP9tp8yZYri4+O1dOlS1aEfBwIAAPg4NrC8QYMGkqSIiIudWzk5OTp06JB69uyp6Ohov22joqJ0++23Ky8vT99++61TTQAAAAgaR0LU/v379d5776lly5bq0qWLpIshSpI6dOgQcB/v/d7tAAAA6pJqjYkK5Ny5cxoxYoRKSko0f/58hYeHS7o4SZWkCifH9E5g5d0ukJKSEpWUlPhu84s+AABQW1xRT1RpaanGjBmjjRs3aty4cRoxYoRT7ZIkzZ07V3Fxcb4lISHB0foAAAC2rEOUMUbjxo3TihUrNHz4cC1atMhvvbcHqqKeJm+vUmWXcZkyZYoKCwt9y4EDB2ybCwAA4Cirr/NKS0uVkZGhZcuWKT09XZmZmQoL889jlxvzdLkxU5Lkdrt90yUAAADUJtXuiSoboIYMGaJXXnnFNw6qrA4dOqh169batGlTuUk1z5w5o40bN6p169Zq3769fesBAABCpFohqrS0VGPHjtWyZcv0k5/8RCtWrAgYoCTJ5XIpIyNDJ0+e1OzZs/3WzZ07V/n5+crIyJDL5bJvPQAAQIhU6+u82bNnKzMzU40bN9aNN96oOXPmlNsmLS1NycnJkqTJkyfrrbfe0vz58/Xpp5+qa9eu2rlzp9atW6fk5GRNnjzZkQcBAAAQbNUKUbm5uZKkkydP6tlnnw24TVJSki9ERUdHKysrS7NmzdLq1auVlZWlli1bauLEiZoxY0a5STgBAADqimqFqMzMTGVmZlbrAHFxcVqwYIEWLFhQrf0AAABqM8cu+wIAAHA1ueIZywEEz8yZMx2t165dO8dq3XvvvY7VQvVt2rTJsVreC8k7ZevWrY7V+vDDDx2r5R2iAtiiJwoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMCCyxhjQt2IqvJ4PIqLiwt1MwAAQD1XWFio2NjYSrehJwoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMACIQoAAMBCtUJUXl6eXnjhBfXr10/XX3+9IiMj1bJlSw0ePFhbtmwpt/3MmTPlcrkCLlFRUY49CAAAgGCLqM7GL730kubNm6d27dopNTVVzZs3V05OjtauXau1a9fqtdde0wMPPFBuv5EjRyopKcn/wBHVOjQAAECtUq0k0717d23cuFG9e/f2u/+jjz7SXXfdpYceekj33Xef3G633/pRo0bpjjvuuOLGAgAA1BbV+jpv0KBB5QKUJPXu3Vt9+vTRiRMn9NlnnznWOAAAgNrKse/UGjRocLFggK/pPvroI23dulXh4eHq1KmT+vbtW663CgAAoC5xJETt379f7733nlq2bKkuXbqUWz99+nS/261atdLy5cuVmppaad2SkhKVlJT4bns8HieaCwAAcMWueIqDc+fOacSIESopKdH8+fMVHh7uW5ecnKzly5crNzdXp0+fVk5Ojp555hkVFBRowIAB2rlzZ6W1586dq7i4ON+SkJBwpc0FAABwhrkCFy5cMMOHDzeSzLhx46q83x//+Ecjydx///2VbnfmzBlTWFjoWw4cOGAksbCwsLCwsLDU6FJYWHjZPGMdokpLS82YMWOMJDN8+HBz4cKFKu9bUlJiIiIiTKtWrap1zMLCwpCfVBYWFhYWFpb6v1QlRFl9nVdaWqqxY8fq5ZdfVnp6ujIzMxUWVvVSkZGRiomJ0alTp2wODwAAEHLVDlGlpaXKyMjQsmXLNGTIEL3yyit+46CqIicnR/n5+eUm4AQAAKgrqhWivD1Qy5Yt009+8hOtWLGiwgBVVFSkXbt2lbs/Pz9fY8eOlSSlp6dbNBkAACD0qjXFwezZs5WZmanGjRvrxhtv1Jw5c8ptk5aWpuTkZB0/flw333yzunXrpi5duqh58+bKy8vTunXrdPz4caWmpmrixImOPRAAAIBgqlaIys3NlSSdPHlSzz77bMBtkpKSlJycrKZNm+rhhx/W5s2b9de//lUFBQWKjo5Wly5dNHz4cGVkZFT7a0AAAIDawmWMMaFuRFV5PB7FxcWFuhkAAKCeKywsVGxsbKXbXPFkmwAAAFcjQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAIAFQhQAAICFOhWijDGhbgIAALgKVCVz1KkQVVRUFOomAACAq0BVMofL1KHundLSUh06dEgxMTFyuVwVbufxeJSQkKADBw4oNjY2iC2ExPmvDXgOQovzH1qc/9Cq6+ffGKOioiK1bt1aYWGV9zVFBKlNjggLC1ObNm2qvH1sbGydfALrC85/6PEchBbnP7Q4/6FVl89/XFxclbarU1/nAQAA1BaEKAAAAAv1MkS53W7NmDFDbrc71E25KnH+Q4/nILQ4/6HF+Q+tq+n816mB5QAAALVFveyJAgAAqGmEKAAAAAuEKAAAAAuEKAAAAAv1KkR98sknuvfeexUfH6/o6Gh1795dr776aqibddVISkqSy+UKuEyYMCHUzasXVqxYofHjx6tbt25yu91yuVzKzMyscHuPx6NJkyYpMTFRbrdbiYmJmjRpkjweT/AaXc9U5zmYOXNmhe+JqKio4Da8HsjLy9MLL7ygfv366frrr1dkZKRatmypwYMHa8uWLQH34T3gnOqe/6vh9V+nZiyvTFZWlvr376/IyEgNHTpUcXFxWrNmjYYNG6bc3FxNnTo11E28KsTFxenRRx8td3+3bt2C35h6aNq0adq3b5+aNWumVq1aad++fRVuW1xcrJSUFO3YsUOpqalKT0/Xzp079fzzz2vDhg3Kzs5WdHR0EFtfP1TnOfAaOXKkkpKS/O6LiKg3//0GzUsvvaR58+apXbt2Sk1NVfPmzZWTk6O1a9dq7dq1eu211/TAAw/4tuc94Kzqnn+vev36N/XAuXPnTLt27Yzb7Tbbt2/33e/xeEznzp1NRESE+eabb0LYwqtDYmKiSUxMDHUz6rV//OMfJjc31xhjzNy5c40ks2zZsoDbTp8+3UgykydPDnj/9OnTa7q59VJ1noMZM2YYSWbDhg3Ba2A99sYbb5iNGzeWu3/jxo2mQYMGpmnTpubMmTO++3kPOKu65/9qeP3Xi6/zPvjgA+3Zs0cPPvigbrnlFt/9MTExevrpp3X+/HktW7YshC0EnNG3b18lJiZedjtjjJYsWaLGjRtr+vTpfuumTJmi+Ph4LV26VIZp4qqtqs8BnDdo0CD17t273P29e/dWnz59dOLECX322WeSeA/UhOqc/6tFvehPy8rKkiT169ev3DrvfR9++GEwm3TVKikp0fLly5WXl6f4+Hj16NFDN998c6ibddXJycnRoUOH1L9//3JfV0RFRen222/Xm2++qW+//VYdOnQIUSuvHh999JG2bt2q8PBwderUSX379r0qZnMOpgYNGkj699dEvAeC69LzX1Z9fv3XixCVk5MjSQHfCPHx8WrWrJlvG9Ssw4cPa9SoUX733X333XrllVfUrFmz0DTqKlTZe6Ls/Tk5OfwBCYJLe0JatWql5cuXKzU1NUQtql/279+v9957Ty1btlSXLl0k8R4IpkDnv6z6/PqvF1/nFRYWSro4qDmQ2NhY3zaoOWPGjFFWVpaOHj0qj8ejzZs365577tG7776rAQMG0G0eRFV5T5TdDjUjOTlZy5cvV25urk6fPq2cnBw988wzKigo0IABA7Rz585QN7HOO3funEaMGKGSkhLNnz9f4eHhkngPBEtF51+6Ol7/9aInCrXDpZ82brvtNv3tb39TSkqKsrOz9c477+hHP/pRiFoHBF9aWprf7fbt22vatGlq0aKFfvazn2nOnDn685//HJrG1QOlpaUaM2aMNm7cqHHjxmnEiBGhbtJV5XLn/2p4/deLnijvJ42KPlF4PJ4KP42gZoWFhWn06NGSpE2bNoW4NVePqrwnym6H4Bo5cqQiIiJ4T1wBY4zGjRunFStWaPjw4Vq0aJHfet4DNety578y9en1Xy9CVNnvti+Vn5+vY8eO8Z13CHnHQp06dSrELbl6VPaeKHs/74vQiIyMVExMDO8JS6WlpRo7dqxefvllpaenKzMzU2Fh/n/OeA/UnKqc/8rUp9d/vQhRKSkpkqT169eXW+e9z7sNgs87k+2lk62h5nTo0EGtW7fWpk2bVFxc7LfuzJkz2rhxo1q3bq327duHqIVXt5ycHOXn5/OesFBaWqqMjAwtW7ZMQ4YM0SuvvOI3DseL90DNqOr5r0x9ev3XixB11113qW3btnr11Ve1Y8cO3/1FRUV65plnFBERUe4XY3DWF198oYKCgnL3Z2dna8GCBXK73Ro0aFDwG3aVcrlcysjI0MmTJzV79my/dXPnzlV+fr4yMjLkcrlC1ML6r6ioSLt27Sp3f35+vsaOHStJSk9PD3az6jRvD8iyZcv0k5/8RCtWrKjwDzjvAedV5/xfLa9/l6knP5nasGGD+vfvL7fbrfT0dMXGxmrNmjX67rvvNGfOHD311FOhbmK9NnPmTM2fP1933XWXkpKS5Ha7tXv3bq1fv15hYWFatGiRMjIyQt3MOm/JkiXKzs6WJH322Wfavn27evbs6fs0nZaW5hvMWVxcrF69evkuedG1a1ft3LlT69atU3JyMpe8sFTV5yA3N1c33HCDunXrpi5duqh58+bKy8vTunXrdPz4caWmpupvf/ubIiMjQ/lw6pSZM2dq1qxZaty4sR555JGAcxKlpaUpOTlZEu8Bp1Xn/F81r/+QzZVeA7Zs2WLuvvtuExcXZxo2bGi6detmVqxYEepmXRWysrLMAw88YNq3b29iYmJMgwYNTJs2bczQoUPNli1bQt28emPkyJFGUoXLjBkz/LYvKCgwEydONAkJCaZBgwYmISHBTJw40RQUFITmAdQDVX0OCgsLzcMPP2y6du1qmjVrZiIiIkxcXJzp1auXWbRokTl//nxoH0gddLlzrwCX4OE94JzqnP+r5fVfb3qiAAAAgqlejIkCAAAINkIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACABUIUAACAhf8Hvona07JrvoYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 3: imgDisp label is 2, x label is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random select 3 examples from imgDisp and testset\n",
    "np.random.seed(42)\n",
    "idx = np.random.choice(len(imgDisp), 3)\n",
    "\n",
    "# Select instances\n",
    "imgDisp_select = [imgDisp[i] for i in idx]\n",
    "x_select = x_test[idx]\n",
    "y_select = y_test[idx]\n",
    "\n",
    "y_select_pred, y_select_proba = predict(x_select, w, b)\n",
    "\n",
    "# Check the selected instances' labels are the same\n",
    "for i in range(len(idx)):\n",
    "    print(f'Sample {i+1}: imgDisp label is {imgDisp_select[i][1]}, x label is {y_select[i]}')\n",
    "\n",
    "    # Display image from imgDisp\n",
    "    fig, ax = plt.subplots(figsize=(7,7))\n",
    "    ax.imshow(imgDisp_select[i][0], cmap='gray')\n",
    "    ax.tick_params(axis='both', which='major', labelsize=ticklabel_size) # Set tick label size\n",
    "    ax.set_title(f\"Label: {imgDisp_select[i][1]}, Prediction: {y_select_proba[i]:.4f}\", fontsize=label_size)\n",
    "\n",
    "    # plt.savefig(f'binary_prediction_{i+1}.png', dpi=300) # Make figure clearer\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d5fb799-c879-4187-b987-7f18430a3afe",
   "metadata": {},
   "source": [
    "### 支持向量机的基本逻辑"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e5f37ac4-9f69-43c1-aef2-06f4b81f5701",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 303.14 seconds\n"
     ]
    }
   ],
   "source": [
    "from sklearn import svm\n",
    "import time\n",
    "\n",
    "# Define SVM classifier\n",
    "mdl_svm = svm.SVC(kernel='linear', probability=True)\n",
    "\n",
    "# Train model\n",
    "start_time = time.time()\n",
    "mdl_svm.fit(x_train, y_train)\n",
    "end_time = time.time()\n",
    "\n",
    "print(f'Training time: {end_time - start_time:.2f} seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c81d92a4-7885-482e-8370-d4b40ea1e81b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision: 0.9755, Recall: 0.9454, Accuracy: 0.9911, F1-Score: 0.9602\n"
     ]
    }
   ],
   "source": [
    "# Make predictions and evaluate the model\n",
    "y_pred_svm = mdl_svm.predict(x_test)\n",
    "y_proba_svm = mdl_svm.predict_proba(x_test) # Output ratio\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred_svm)\n",
    "precision = precision_score(y_test, y_pred_svm)\n",
    "recall = recall_score(y_test, y_pred_svm)\n",
    "f1 = f1_score(y_test, y_pred_svm)\n",
    "\n",
    "print(f'Precision: {precision:.4f}, Recall: {recall:.4f}, Accuracy: {accuracy:.4f}, F1-Score: {f1:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "689a2d53-608f-4c6f-9fdb-ef46d2367007",
   "metadata": {},
   "source": [
    "### 决策树和随机森林"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08c93438-6909-43c0-87d4-315a0ce0f4c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 28.24 seconds\n"
     ]
    }
   ],
   "source": [
    "# Define DecisionTree classifier\n",
    "mdl_dt = tree.DecisionTreeClassifier()\n",
    "\n",
    "# Train model\n",
    "start_time = time.time()\n",
    "mdl_dt.fit(x_train, y_train)\n",
    "end_time = time.time()\n",
    "\n",
    "print(f'Training time: {end_time - start_time:.2f} seconds')\n",
    "\n",
    "# Define Random Forest classifier\n",
    "mdl_rf = RandomForestClassifier(n_estimators=100)\n",
    "\n",
    "# Train model\n",
    "start_time = time.time()\n",
    "mdl_rf.fit(x_train, y_train)\n",
    "end_time = time.time()\n",
    "\n",
    "print(f'Training time: {end_time - start_time:.2f} seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "334bf22a-22a8-4d2c-8252-59feeab8746a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision: 0.9123, Recall: 0.9251, Accuracy: 0.9814, F1-Score: 0.9186\n",
      "Precision: 0.9897, Recall: 0.9348, Accuracy: 0.9915, F1-Score: 0.9615\n"
     ]
    }
   ],
   "source": [
    "y_pred_dt = mdl_dt.predict(x_test)\n",
    "y_proba_dt = mdl_dt.predict_proba(x_test) # Output ratio\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred_dt)\n",
    "precision = precision_score(y_test, y_pred_dt)\n",
    "recall = recall_score(y_test, y_pred_dt)\n",
    "f1 = f1_score(y_test, y_pred_dt)\n",
    "\n",
    "print(f'Precision: {precision:.4f}, Recall: {recall:.4f}, Accuracy: {accuracy:.4f}, F1-Score: {f1:.4f}')\n",
    "\n",
    "y_pred_rf = mdl_rf.predict(x_test)\n",
    "y_proba_rf = mdl_rf.predict_proba(x_test) # Output ratio\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred_rf)\n",
    "precision = precision_score(y_test, y_pred_rf)\n",
    "recall = recall_score(y_test, y_pred_rf)\n",
    "f1 = f1_score(y_test, y_pred_rf)\n",
    "\n",
    "print(f'Precision: {precision:.4f}, Recall: {recall:.4f}, Accuracy: {accuracy:.4f}, F1-Score: {f1:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "61e3528a-8894-4912-8aa7-1dfdfdc5827e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_roc_curve_base():\n",
    "    \"\"\"Plots the ROC curve and computes AUC.\"\"\"\n",
    "    global label_size, ticklabel_size # Set global variables of font size\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "    ax.plot([0, 1], [0, 1], color='grey', lw=2, linestyle='--')\n",
    "    ax.set_xlim([0.0, 1.0])\n",
    "    ax.set_ylim([0.0, 1.0])\n",
    "    ax.tick_params(axis='both', which='major', labelsize=ticklabel_size) # Set tick label size\n",
    "\n",
    "    ax.set_xlabel('False Positive Rate (FPR)', fontsize=label_size)\n",
    "    ax.set_ylabel('True Positive Rate (TPR)', fontsize=label_size)\n",
    "\n",
    "    return fig, ax\n",
    "\n",
    "def add_roc_curve(ax, y_true, y_proba, curve_color, curve_label):\n",
    "    \"\"\"Plots the ROC curve and computes AUC.\"\"\"\n",
    "\n",
    "    fpr, tpr, thresholds = roc_curve(y_true, y_proba)\n",
    "    roc_auc = auc(fpr, tpr)\n",
    "\n",
    "    roc = ax.plot(fpr, tpr, color=curve_color, lw=2, label=f'{curve_label} (AUC = {roc_auc:.4f})')\n",
    "\n",
    "    return roc_auc, fpr, tpr, thresholds\n",
    "\n",
    "fig, ax = plot_roc_curve_base()\n",
    "\n",
    "roc_auc_logic, fpr_logic, tpr_logic, thresholds_logic = add_roc_curve(ax, y_test, y_proba, color_list[0], 'Logic Regression')\n",
    "roc_auc_logic, fpr_logic, tpr_logic, thresholds_logic = add_roc_curve(ax, y_test, y_proba_svm[:,1], color_list[1], 'SVM')\n",
    "roc_auc_logic, fpr_logic, tpr_logic, thresholds_logic = add_roc_curve(ax, y_test, y_proba_dt[:,1], color_list[2], 'Decision Tree')\n",
    "roc_auc_logic, fpr_logic, tpr_logic, thresholds_logic = add_roc_curve(ax, y_test, y_proba_rf[:,1], color_list[3], 'Random Forests')\n",
    "\n",
    "plt.legend(loc=\"lower right\", fontsize=ticklabel_size)\n",
    "plt.savefig('1g', dpi=300) # Make figure clearer\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "534fa0b9-3736-4d83-979c-4ad9c4aeab59",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Extract features and labels from trainset\n",
    "x_train = []\n",
    "y_train = []\n",
    "for image, label in trainset:\n",
    "    x_train.append(image.numpy())\n",
    "    y_train.append(label)\n",
    "\n",
    "x_train = np.array(x_train)\n",
    "y_train = np.array(y_train)\n",
    "\n",
    "# Extract features and labels from trainset\n",
    "x_test = []\n",
    "y_test = []\n",
    "for image, label in testset:\n",
    "    x_test.append(image.numpy())\n",
    "    y_test.append(label)\n",
    "\n",
    "x_test = np.array(x_test)\n",
    "y_test = np.array(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65a7a936-b8a9-43a6-bf87-83ff9b01eb4a",
   "metadata": {},
   "source": [
    "### 一对多（One-vs-Rest）方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9c4bbffc-a7ce-4da7-9153-c12e89f7c635",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 10.52 seconds\n",
      "Accuracy: 0.8536\n"
     ]
    }
   ],
   "source": [
    "# Define logic multi-classifier\n",
    "mdl_logic_ovr = OneVsRestClassifier(LogisticRegression(max_iter=1000))\n",
    "\n",
    "# Train model\n",
    "start_time = time.time()\n",
    "mdl_logic_ovr.fit(x_train, y_train)\n",
    "end_time = time.time()\n",
    "\n",
    "print(f'Training time: {end_time - start_time:.2f} seconds')\n",
    "\n",
    "# Make predictions and evaluate the model\n",
    "y_pred_logic_ovr = mdl_logic_ovr.predict(x_test)\n",
    "y_proba_logic_ovr = mdl_logic_ovr.predict_proba(x_test) # Output ratio\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred_logic_ovr)\n",
    "print(f'Accuracy: {accuracy:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "e5b17332-5ff2-4e16-9e8c-bb2c6810a269",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training class 0, Training time: 1.05 seconds\n",
      "Training class 1, Training time: 0.60 seconds\n",
      "Training class 2, Training time: 0.99 seconds\n",
      "Training class 3, Training time: 1.02 seconds\n",
      "Training class 4, Training time: 0.72 seconds\n",
      "Training class 5, Training time: 1.49 seconds\n",
      "Training class 6, Training time: 0.94 seconds\n",
      "Training class 7, Training time: 1.11 seconds\n",
      "Training class 8, Training time: 1.58 seconds\n",
      "Training class 9, Training time: 1.25 seconds\n"
     ]
    }
   ],
   "source": [
    "# Get class list: 0, 1, ..., 9\n",
    "class_list = np.sort(np.unique(y_train))\n",
    "\n",
    "# Create model list\n",
    "mdl_logic_list = []\n",
    "for c in class_list:\n",
    "    mdl_logic_list.append(LogisticRegression(max_iter=1000))\n",
    "\n",
    "# Train models seperately\n",
    "for i in range(len(class_list)):\n",
    "    start_time = time.time()\n",
    "    mdl_logic_list[i].fit(x_train, (y_train == class_list[i]).astype(int))\n",
    "    end_time = time.time()\n",
    "    print(f'Training class {class_list[i]}, Training time: {end_time - start_time:.2f} seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9717c302-26fd-475e-a65c-d644dbfc9d19",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'class_list' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[29], line 5\u001b[0m\n\u001b[0;32m      2\u001b[0m fig, ax \u001b[38;5;241m=\u001b[39m plot_roc_curve_base()\n\u001b[0;32m      4\u001b[0m \u001b[38;5;66;03m# Draw ROC of individual classifier\u001b[39;00m\n\u001b[1;32m----> 5\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(class_list)):\n\u001b[0;32m      6\u001b[0m     \u001b[38;5;66;03m# Make predictions and evaluate the model\u001b[39;00m\n\u001b[0;32m      7\u001b[0m     y_test_trans \u001b[38;5;241m=\u001b[39m (y_test \u001b[38;5;241m==\u001b[39m class_list[i])\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mint\u001b[39m)\n\u001b[0;32m      8\u001b[0m     y_proba \u001b[38;5;241m=\u001b[39m mdl_logic_list[i]\u001b[38;5;241m.\u001b[39mpredict_proba(x_test) \u001b[38;5;66;03m# Output ratio\u001b[39;00m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'class_list' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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5+fD19cWbb76JsWPHGn2NtLQ0LF68GFu2bEFcXByUSiUaNGiAiRMnYurUqbC3tze5PiIiIrJOOp0Ohw4dwuHDhwEAu3fvxrBhwySuiqyJTNAn4efIycnBv//9b3z//fd48uSJGKBtbGzQrFkzeHh4oHr16nBwcEBKSgpSUlIQFxeHpKSkghv9L2gHBgbi888/R5cuXUpVaHR0NIKCgmBnZ4fRo0dDpVJh8+bNiIuLw+eff44PP/zwuddIS0tDx44dERsbi+7du6Nr167Iy8vD7t27cfv2bQQGBmLfvn1GTzzIyMiASqVCeno6Z/8SERFZqczMTERERODOnTtiW6NGjTB69GjY2HCkrLWrqLxmVKhes2YN5s6di8TERAiCgFatWmHMmDHo2bMnOnbsWGLvbnx8PE6ePImtW7di27ZtePr0KWQyGV588UUsWrQIdevWfW6RGo0GzZs3x71793D8+HG0b98eQMEPgZ+fH65fv44rV66gSZMmJV5n0aJFeP/99zF79mwsXrxYbM/Pz0f37t1x+vRpHDp0CD179nxuTQBDNRERkbW7desWIiMj8fTpUwAFnYCBgYHw9/cv9Jd3sk4VldeM6pKdMmUKkpKSMH36dPz555+4ePEi5syZA39//+cOl/Dx8cFLL72EDRs24PHjx1izZg1atGiBjRs3YvXq1UYVeeDAAdy+fRtjx44VAzUAVKtWDXPnzoVGozHqWrGxsQCA4OBgg3Y7Ozv069cPAPD48WOjaiIiIiLrpdPpEBUVhV9//VUM1C4uLpg0aRK6d+/OQE2lZtTfNGbMmIEPP/zQqF7lkjg6OmLChAl4+eWXERYWBrVabdTroqOjARQsafN3+rZDhw499zq+vr4AgD/++AN9+/YV29VqNaKiouDg4AA/Pz+jaiIiIiLrlJ6ejoiICCQkJIhtTZo0wfDhw+Ho6ChhZWTNjArVP/30k1lvqh/+YaybN28CQJHDO9zc3ODh4SGeU5KpU6di3bp1+Pe//40zZ86gc+fOyMvLwx9//IHU1FRs2LABderUKfb1eXl5yMvLEz/PyMgw+j0QERGRZbh8+bIYqOVyOfr06QM/Pz/2TlOZWMXo+/T0dACASqUq8riLiwvu3bv33Os4ODggOjoaM2bMwPr168Xebblcjn/84x/o3r17ia//8ssvsWDBglJWT0RERJbEz88Pt2/fxpMnTxAaGgpvb2+pS6JKoEL317x06VJF3q6Q5ORk9OvXDydOnMDOnTuRlpaGhw8f4ueff8bq1avRtWtXpKamFvv6OXPmID09Xfx49s9GREREZJny8/MNPpfJZBg5ciRmzJjBQE1mUyGh+tq1a3jxxRfRoUMHk16v76HW91j/nX5W5/O89dZbOHbsGCIiIhAcHAyVSoVatWph2rRpWLRoEWJjY/Htt98W+3qlUgkXFxeDDyIiIrJc165dw3fffWewXB4AODk5wcHBQaKqqDIq11B969YtvPzyy2jdujUiIiKg0+lMuo5+LHVR46ZTU1ORnJz83OX0AGDnzp2oXr062rRpU+hYYGAgAODs2bMm1UhERESWQ6PRYPfu3di4cSOePn2KiIgIcZUPovJQ6lC9evVqdO/eHW5ubnBxcUG7du3w/fffG+ysmJycjFdffRUtW7bEhg0boNVqUatWLfzrX/8yqciAgAAAwN69ewsd07fpzylJfn4+MjIyCv0ZCIC4SY1SqTSpRiIiIrIMKSkpWLVqFU6dOiW21a1b1+jN3YhMUarvrhkzZmDq1Kk4fvw40tPTkZWVhYsXL2L27NniVuGHDx9G69atsWzZMmg0GtSrVw9LlixBXFwc3nnnHZOK7NOnDxo2bIgNGzbg/PnzYntmZiYWLlwIGxsbTJo0SWxPTk7GtWvXkJycbHAdf39/aDQaLFy40KA9Ly9PbOvdu7dJNRIREZH0Ll++jGXLluHBgwcAAIVCgeDgYISGhj53bw2isjB6m/K9e/diwIABAAB3d3d07doVgiDg1KlTePLkCWQyGX788Ue89957yMrKQqNGjfDxxx9j/PjxUCgUZS704MGDCAoKglKpxJgxY+Di4iJuU/7ZZ5/ho48+Es+dP38+FixYgHnz5mH+/Pli+/nz59GzZ09kZmaiS5cu8Pf3R25uLvbs2YPY2Fh07NgRMTExRv/QcUdFIiIiy6DRaLBnzx6cOXNGbKtevTpGjRoFT09PCSsjqVVUXjN6ST39joU9e/bEli1b4OrqCqBgTPOwYcMQExODf/zjHxAEAfPnz8eHH34IGxvzrdjXu3dvxMTEYN68edi0aRPy8/Ph6+uLhQsXYty4cUZdo127djh79iy+/PJL7N+/H0uWLIGNjQ0aN26MBQsW4J133uFvsURERFbmyZMnCA8Px8OHD8W21q1bY9CgQRzWSRXG6J7qxo0bIy4uDmfOnDHYKhwomNzXuXNnyGQyvPvuu/jqq6/KpVhLw55qIiIi6T1+/BjLly+HRqOBjY0NBg4ciPbt23MzFwJQcXnN6FDt7OwMtVqN3NzcQt+kOp0O9vb20Gq1uHnzJho2bFguxVoahmoiIiLL8Oeff+LYsWMIDQ1FrVq1pC6HLIjFDf94+vQpPD09i/ytTy6Xw93dHY8fP0b9+vXNWiARERHRs548eQKVSmUwzLRdu3Zo3bq1WYeeEpWG2deWMcekRCIiIqKiXLhwAUuXLsW+ffsM2mUyGQM1SYrffURERGTx8vPzsXv3bnFp3VOnTqFx48ZGbf5GVBFKFapTUlLEnQeLOgag2ONAwW+R+/fvL80tiYiIqIp7/PgxwsLCDPafaN++PXx8fKQriuhvjJ6oKJfLIZPJYOTphjf53+tkMpnBzovWjhMViYiIyo8gCPjzzz+xe/duaDQaAICdnR0GDx6M1q1bS1wdWQuLm6jYs2dPLk1DREREFSIvLw87d+7EpUuXxLZatWph1KhRcHd3l7AyoqIZHaqjo6PLsQwiIiKiAunp6Vi3bh2ePHkitnXs2BEDBgzgZESyWPzOJCIiIovi7OwMR0dHPHnyBHZ2dhg6dCh8fX2lLouoRAzVREREZFEUCgVCQkKwfft2BAcHo3r16lKXRPRcpQ7Vf/31F3766SecPn0aGRkZqF69Orp164ZZs2ahUaNG5VEjERERVWKJiYmQy+Xw9PQU21QqFcaPHy9hVUSlY/TqHwCwatUqzJw5U1zBQ7+iB1AwG/e3337D8OHDy6VQS8TVP4iIiEwnCAJOnTqFffv2wcXFBTNmzIBSqZS6LKpkKiqvGb2j4tWrV/Hqq69Co9FAEAR4enqic+fO8PDwgCAIyMvLw4QJE5CYmFhuxRIREVHlkJOTg02bNuGPP/6AVqtFamoqjh49KnVZRCYzOlT/+OOPUKvV8PT0xL59+3D//n2cPHkSjx49wqZNm+Di4oLs7GysWLGiPOslIiIiK3f//n0sW7YM165dE9u6deuGgIAACasiKhujx1QfOnQIMpkMP/zwA/r06WNwLDQ0FA8ePMA///lPHD582OxFEhERkfUTBAEnTpxAVFQUdDodAMDe3h7Dhw9Hs2bNJK6OqGyMHlOtUqmQnZ2N7OzsIsc73b17Fz4+PmjcuDFu3Lhh9kItEcdUExERGefp06fYunWrQUaoW7cuQkJCoFKpJKyMKjuL21ExMzMTNWvWLHYCQb169QAA2dnZ5qmMiIiIKgWNRoMVK1YgNTVVbPP390fv3r2hUCgkrIzIfIweUw0AcvnzTy/FYiJERERUBdjY2KBLly4AAEdHR4wbNw59+/ZloKZKhZu/EBERUbnr2rUrcnNz0aFDBw6ZpEqpVKE6PT0dU6ZMMfkcmUyGlStXluaWREREZGXu3LmDxMRE+Pn5iW0ymQy9evWSriiicmb0REW5XC5u9GIK/UYx+o1jKgNOVCQiIvp/Op0OMTExiI6OhiAIGD9+PHdbJslZ3ETFevXqlSlUExERUeWVlZWFyMhIxMbGim1//vknQzVVGUaH6vj4+HIsg4iIiKxVXFwcIiIixBXAZDIZAgIC0KNHD4krI6o4nKhIREREJtHpdDh06JDBxm/Ozs4ICQmBj4+PdIURScDoUD1lyhS4urpi8eLF5VkPERERWYHMzExs3rzZ4C/ZjRo1wogRI+Dk5CRdYUQSKdVERU9PTyQmJpZ3TVaDExWJiKiqWr9+PW7fvg2gYLhH79690b17d86/IotTUXmtVJu/EBEREQHAwIEDYWdnh2rVqmHSpEno0aMHAzVVaRxTTURERM+lXxpXz93dHWPGjEHNmjXh6OgoYWVEloE91URERFSimzdvYu3atVCr1QbtPj4+DNRE/8NQTUREREXSarXYt28fNmzYgPj4eOzevVvqkogsVqmGf+Tn5+PIkSMwcm5jkXr27Gnya4mIiKhipKWlISIiAvfu3RPbnj59Cq1WC4VCIWFlRJapVKE6NTUVvXr1MvlmMpkMGo3G5NcTERFR+bt27Rq2bt2K3NxcAAUrgPXr1w9du3blZESiYpR6omJZeqmJiIjIcumHe5w8eVJsc3V1RWhoKOrUqSNhZUSWr1Sh2s3NDREREeVVCxEREUkkNTUV4eHhBvtRtGjRAkOHDoW9vb2ElRFZh1KFajs7OwQEBJRXLURERCSRy5cvi4FaoVAgKCgInTp14nAPIiNxnWoiIiLCCy+8gNjYWKSnpyM0NBS1a9eWuiQiq8JQTUREVAXl5eVBqVSKn8vlcoSEhMDGxsagnYiMw3WqiYiIqpi//voL3377LRISEgzanZycGKiJTMRQTUREVEWo1Wps374dERERyM3NRXh4OJ4+fSp1WUSVgtHDP3r27AkPD4/yrIWIiIjKSXJyMsLCwvD48WOxzcfHBzY2HAlKZA5G/yRFR0eXYxlERERUXi5cuICdO3dCrVYDAGxsbBAcHIx27dpxdQ8iMzEqVOfk5MDBwcHsN3/69CkcHR3Nfl0iIiIC8vPzsXv3bpw/f15sq1GjBkaNGoUaNWpIVxhRJWTUmGofHx8sXrxY3K60rM6cOYPBgwfj3//+t1muR0RERIaSkpKwYsUKg0Ddrl07TJs2jYGaqBwYFarz8vLw7rvvwsfHBx988AEuXbpU6htlZWVh7dq16Nu3L7p27Ypdu3bB1dW11NchIiKi59PpdEhNTQUA2NraYsSIERg2bBhsbW0lroyocpIJgiA876SUlBTMmzcPS5cuhVarBVCwdWnPnj3RpUsXtG3bFjVq1ED16tWhVCqRmpqKlJQUxMbG4tSpUzh58iQOHTqEnJwcCIKAli1bYtGiRQgODi73N1ieMjIyoFKpkJ6eDhcXF6nLISIiMnD27FmcPn0aoaGhXGyAqqyKymtGhWq9mzdv4t///jd+++03ZGZmGj25QX+LLl26YNasWRg3bhzkcutfzY+hmoiILEVSUhKqV68OhUIhtgmCAK1WyxU+qEqzyFCtl52djd9++w1//PEHYmJiDJbneZaNjQ06dOiAXr16YcyYMWjbtm2ZC7YkDNVERCQ1QRBw9uxZ/PHHH+jcuTOCgoKkLonIolh0qP67uLg4JCYmIikpCbm5uXB3d0eNGjXQtGnTSr26B0M1ERFJKS8vD9u3b8fly5fFtpdffhkNGzaUsCoiy1JRec0sfw9q0KABGjRoYI5LERERkREePHiAsLAwcTIiUDDMsl69ehJWRVR1cZAVERGRFREEAadPn8bevXvFxQOUSiWGDRuGFi1aSFwdUdXFUE1ERGQlcnNzsW3bNly9elVs8/LyQmhoKNzc3CSsjIgYqomIiKxAamoq1q5di7S0NLGtW7du6Nu3r8GKH0QkDYZqIiIiK+Di4gJnZ2ekpaXB3t4ew4cPR7NmzaQui4j+h6GaiIjICigUCoSEhGDXrl0IDg7mrsREFoahmoiIyAIlJCTA1tYWnp6eYpurqyvGjh0rYVVEVBzr39aQiIioEhEEAUePHsXq1asRFhaGvLw8qUsiIiMwVBMREVmI7OxsbNiwAVFRURAEASkpKTh58qTUZRGRETj8g4iIyALcuXMHERERyMzMFNt69OiB7t27S1gVERnLbKFaEAQ8efIET58+5W5ORERERhIEAUeOHEF0dDQEQQAAODk5YcSIEWjUqJHE1RGRscocqs+dO4fPPvsMUVFRyM7Ohkwmg0ajEY+npqbigw8+gEwmw/fffw87O7uy3pKIiKhSyMrKQmRkJGJjY8U2Hx8fjBw5EtWqVZOwMiIqrTKF6nXr1mHq1KlQq9XFnuPm5oa4uDjs378fQ4YMwaBBg8pySyIiokpBrVZjxYoVSE9PBwDIZDIEBASgR48ekMs55YnI2pj8U3v16lVMmzYNarUab7zxBs6cOQMPD48iz50wYQIEQcDWrVtNLpSIiKgysbW1RZcuXQAAzs7OmDBhAgICAhioiayUyT3VixcvRn5+PmbNmoVvv/0WAIrdJjUwMBAAcPz4cVNvR0REVOn4+flBrVajU6dOcHJykrocIioDk38dPnDgAGQyGd5///3nnuvl5QVHR0fcvXvX1NsRERFZtdu3bxfqXNIP+WCgJrJ+JvdUJyYmwsnJCd7e3kad7+DgII4bIyIiqip0Oh0OHjyImJgYAICnpycaNGggcVVEZG4mh2qlUonc3FwIggCZTFbiuTk5OUhLS4Orq6uptyMiIrI6GRkZiIiIMPhL7cWLFxmqiSohk4d/+Pj4QK1W4+bNm889d9euXdBqtWjZsqWptyMiIrIqN2/exM8//ywGaplMhr59+2Lo0KESV0ZE5cHkUD1gwAAIgoDvvvuuxPOePHmC9957DzKZjMvpERFRpafVarFv3z5s2LABOTk5AACVSoXJkyfD39//uX/dJSLrZHKonj17NpydnfHzzz9jwYIFBtuqAgVDPjZs2IBOnTohLi4O7u7umDlzZpkLJiIislRpaWlYs2YNjh07JrY1a9YMM2bMQN26dSWsjIjKm0zQ74lqgh07diA0NBRqtRq2trbQ6XTQarVo3rw5YmNjkZ+fD0EQoFQqsWPHDvTp08ectUsuIyMDKpUK6enpcHFxkbocIiKS2C+//IL4+HgAgFwuR79+/dC1a1f2ThNJqKLyWplWmB88eDAOHz6Mjh07Ij8/HxqNBoIg4OrVq8jLy4MgCGjfvj0OHz5c6QI1ERHR3w0aNAi2trZwdXXFlClT0K1bNwZqoiqiTD3Vz7p48SJiYmKQmJgIrVYLT09P+Pv7o1OnTua4vEViTzURUdVW1ApY8fHx8PT0hL29vURVEdGzKiqvmS1UV0UM1UREVdeVK1dw6tQpjBs3Dra2tlKXQ0TFsPjhH2vXrkVYWJjR52/evBlr16419XZEREQWQaPRYNeuXQgLC8OdO3ewZ88eqUsiIgtgck+1XC5H7dq1cf/+faPOb9CgARISEqDRaEy5nUViTzURUdWSkpKCsLAwPHz4UGxr1aoVRowYAbm8TNOUiKicVFReM3lHRaBgLFl5nk9ERGQp/vrrL2zfvh35+fkAAIVCgYEDB6JDhw6cjEhEZQvVpZGRkQE7O7uKuh0REZFZqNVq/PHHHzh37pzY5u7ujlGjRqFWrVoSVkZElqRCQvXx48eRmpqKBg0aVMTtiIiIzCI5ORlhYWF4/Pix2NamTRsMGjSIHUVEZMDoUP3LL7/gl19+MWhLSUlBYGBgsa8RBAFpaWm4fPkyZDIZ+vbta3qlAE6fPo158+bh+PHjyM/Ph6+vL958802MHTu2VNfJzMzEN998g4iICMTGxsLOzg4NGzbEsGHDMG/evDLVSERElcfly5fFQG1jY4Pg4GC0a9eOwz2IqBCjQ3V8fDyio6MN2vLz8wu1FadZs2aYP39+KUozFB0djaCgINjZ2WH06NFQqVTYvHkzxo0bh/j4eHz44YdGXefu3bsIDAxEbGws+vbti0GDBiEvLw+3bt1CREQEQzUREYl69OiB+Ph4ZGdnIzQ0FDVr1pS6JCKyUEav/nHo0CGDAL1gwQI4Ozvj7bffLvY1crkcLi4uaNWqFXr16gWFQmFSkRqNBs2bN8e9e/dw/PhxtG/fHkBBj7Ofnx+uX7+OK1euoEmTJiVeR6vVws/PD3/99Rd27tyJ3r17F7qPjY3xI2K4+gcRUeWSm5tbaNOW7Oxs2NracrgHkZWy+M1f5HI5PD09kZiYaO6aCtm7dy+CgoIwefJkrFq1yuDYxo0bMXr0aMyZMwdffPFFidfRnzt37lx8+umnZa6LoZqIqHIQBAHnz5/Hnj17MH78eHh7e0tdEhGZicUvqRcXF2dyz3Np6XvI+/fvX+iYvu3QoUPPvc7GjRsBAKNGjUJCQgJ27tyJtLQ0NGrUCAMHDoSzs7P5iiYiIquQn5+PnTt34uLFiwCA8PBwzJgxAw4ODhJXRkTWxORQXb9+fXPWUaKbN28CQJHDO9zc3ODh4SGeU5IzZ84AAGJiYjB79mzk5eWJx2rUqIFNmzahV69exb4+Ly/P4DUZGRnGvgUiIrJAjx49QlhYGJ48eSK2NWrUqFRDAYmIgDJsU16R0tPTAQAqlarI4y4uLuI5JdHP4H799dfx5ptvIiEhAUlJSfj++++Rnp6O4cOH48GDB8W+/ssvv4RKpRI/6tata8K7ISIiqQmCgLNnz2L58uVioLazs0NISAiGDBkCW1tbiSskImtT5lB94cIFTJ8+HS1btoSLiwsUCkWxH1L/5q/T6QAAgwcPxldffQVvb294eHjg9ddfx+zZs5Geno6VK1cW+/o5c+YgPT1d/EhISKio0omIyEzy8vKwefNm7NixA1qtFgDg6emJ6dOno1WrVhJXR0TWqkwpd8mSJXjrrbeg1WrLdQtyfQ91cb3R+gHoxlwnOTkZQ4cOLXRsyJAh+Ne//iUOESmKUqmEUqk0smoiIrI0Dx8+RFhYGFJSUsS2zp07o3///pJ3/BCRdTO5p/rkyZP45z//Ca1Wi9deew27du0CAFSvXh1RUVFYv349Jk2aBDs7O3h4eGDDhg04cOCASffSj6Uuatx0amoqkpOTn7ucHlCwVjYAuLq6Fjqmb8vJyTGpRiIisg76DhqlUolRo0YhODiYgZqIyszkUP39999DEAT885//xA8//IABAwYAKBiTFhgYiLFjx2LVqlU4ceIEZDIZ5s6diw4dOph0r4CAAAAFS+v9nb5Nf05J9Ls/XrlypdAxfZuPj49JNRIRkeXz9PREUFAQvLy8MGPGDLRs2VLqkoiokjB5nWofHx8kJCQgNjZWXAlELpejVq1ahSb7bdq0CaNHj8bHH39s0vrQGo0GzZo1w/3793HixAm0a9cOgOHmL5cvX0bTpk0BAMnJyUhOToaHhwc8PDzE68TFxaFFixZQqVQ4d+4c6tSpI16nZ8+eOH/+PKKiotCnTx+j6uI61URElu3Ro0fw8PAwWAJWEATodLoKWxaWiKRVUXnN5J7qR48eQalUGiytJ5fLkZubW+jcESNGwNbWFps3bzbpXjY2NlixYgV0Oh169OiB6dOn45133kHbtm1x+fJlzJ8/XwzUQMFY7xYtWmDJkiUG12nQoAG+/vprPH78GG3btsW0adPwj3/8A23atMH58+cxffp0owM1ERFZLkEQcOLECSxbtqzQ0EOZTMZATURmZ/IgMkdHR2g0GoO2atWqISMjA3l5eQYT+mxtbeHo6Ig7d+6YXGjv3r0RExODefPmYdOmTcjPz4evry8WLlyIcePGGX2d119/HT4+Pvj666/x+++/Q6PRwNfXFx9++CGmTZtmcn1ERGQZcnJysHXrVly/fh0AcOzYMTRp0oTD+4ioXJk8/KNNmza4fPkyUlNTxa70Tp064c8//8ShQ4fQvXt38dzExER4e3vD0dERWVlZ5qncAnD4BxGRZUlISEBERITBalEvvPACAgMD2TtNVEVZ/PCPNm3aAIDYEwAAvXr1giAI+PTTT8VhIPn5+XjjjTcAAK1bty5LrUREREUSBAFHjx7FmjVrxEDt4OCAMWPGoF+/fgzURFTuTA7VgwcPhiAI2Lhxo9g2a9YsKJVK7N+/H97e3vD390edOnUQGRkJmUyGf/zjH2YpmoiISO/p06f47bffEBUVJW7yVa9ePcycOdNgvg0RUXkyeUx1cHAw5s2bB09PT7GtQYMG2LBhAyZPnoyUlBQcP34cQMEExnfffbdUY5+JiIie58mTJ/jll1+QmZkptnXv3h29e/eGXF7mTYOJiIxm8pjqkqSkpGDXrl1ISEiASqVC//790bhxY3PfRnIcU01EJC2tVotVq1YhMTERjo6OGDlyJBo1aiR1WURkQSoqr5VLqK4qGKqJiKSXmpqKvXv3Ijg4GNWqVZO6HCKyMBY/UbG0kpOT8c4771TU7YiIqBKKj4/Ho0ePDNrc3Nzw0ksvMVATkaTKPVSnpqbiww8/RMOGDfGf//ynvG9HRESVkE6nQ3R0NNauXYuwsDDk5+dLXRIRkQGTJireunULly9fhlarRcOGDcVtw5+VlZWFb775Bt9++y0yMzMhCILBhjBERETGyMzMRGRkJOLi4gAUTE48ffo0/P39Ja6MiOj/lSpUJyQkYPz48YiJiTFob9euHX799Vc0b94cALB27Vq8++67SE5OhiAIcHR0xLRp0zj8g4iISuX27duIjIxEdnY2gIItxnv16gU/Pz+JKyMiMmR0qH769Cl69+6NuLg4/H1u459//om+ffvi2rVrmDNnDv773/9CEASoVCrMmjULb775Jjw8PMxePBERVU764R5HjhwR26pVq4aQkBDUr19fwsqIiIpmdKheunQpYmNjIZPJMGXKFAwYMACCIOCPP/7A6tWr8eDBA4SGhmLv3r1wcHDAu+++i7feeourYhARUalkZGQgIiICd+/eFdsaN26M4cOHw8nJScLKiIiKZ3So3rZtG2QyGT766CN8+umnYvuoUaPg5eWFzz//HPv27UPdunWxd+9eNGvWrFwKJiKiyis/Px/Lly9HVlYWgILhHn369MELL7wAmUwmcXVERMUzevWPK1euAADeeOONQsf++c9/iv+9aNEiBmoiIjKJnZ0dunbtCgBwcXHB5MmT4e/vz0BNRBbP6J7q1NRUVKtWrcix0R4eHqhWrRqysrLQp08fsxZIRERVi7+/P3Q6HTp37gwHBwepyyEiMorRPdUajQaOjo7FHtcf44REIiIy1vXr13H8+HGDNplMhp49ezJQE5FVMWmdaiIiorLQarWIiorCiRMnIJPJULt2bfj4+EhdFhGRyUoVqrVaLRISEgotqac/BqDY43r16tUrZYlERFSZpKamIiIiAvfv3wcACIKAy5cvM1QTkVUrVahOTk5+7j96JR2XyWTQaDSluSUREVUiV69exdatW5GXlwcAUCgU6N+/Pzp37ixxZUREZVOqUF1SDzQREVFxNBoN9u7di9OnT4ttbm5uCA0NhZeXl4SVERGZh9GhevXq1eVZBxERVVIpKSkIDw/HgwcPxDZfX18MHjwY9vb2ElZGRGQ+RofqiRMnlmcdRERUCQmCgC1btoiBWqFQYMCAAejYsSPXniaiSsXoJfWIiIhKSyaTYciQIbC1tYW7uzumTp2KTp06MVATUaXDJfWIiMisBEEwCM01atTAuHHj4OnpCaVSKWFlRETlhz3VRERkNhcvXsSaNWsKrfRUv359BmoiqtQYqomIqMzUajW2bduGyMhI3L17F3v37pW6JCKiCsXhH0REVCZJSUkICwtDUlKS2KZWqwsNAyEiqswYqomIyGTnz5/Hrl27oFarAQC2trYYNGgQ2rZtK3FlREQVi6GaiIhKLT8/H7t27cKFCxfEtpo1a2LUqFHw8PCQsDIiImkwVBMRUak8evQI4eHhSE5OFts6dOiAAQMGwNbWVsLKiIikw1BNRESlcuXKFTFQ29nZYfDgwWjdurXEVRERSYuhmoiISiUgIADx8fHIz89HaGgo3N3dpS6JiEhyZgnV27Ztw549e3Dnzh3k5ORg//794rHs7GxcuHABMpkMfn5+5rgdERFVoJycHDg4OIify+VyvPjii1AqlbCxYd8MERFQxlCdkJCAkSNH4ty5cwAK76IFAEqlEmPGjMG9e/dw/vx5/omQiMhKCIKAM2fOICoqChMnToSXl5d4zMnJScLKiIgsj8mbvzx9+hT9+/fH2bNnUadOHcyaNavIf2RtbGwwdepUCIKArVu3lqlYIiKqGLm5uQgPD8euXbuQn5+PsLAw5ObmSl0WEZHFMjlU//jjj7h+/To6dOiAq1ev4vvvv4ezs3OR5w4bNgwAuMMWEZEVSExMxNKlS3HlyhWxrVmzZhzqQURUApP/hQwPD4dMJsPixYuf+2fAVq1awcbGBjdu3DD1dkREVM4EQcDJkyexb98+6HQ6AIC9vT2GDRuG5s2bS1wdEZFlMzlUX79+HQqFAv7+/s89Vy6XQ6VSITU11dTbERFROcrJycG2bdtw7do1sc3b2xshISFwdXWVrjAiIithcqjOy8uDg4MDFAqFUednZ2dDqVSaejsiIion9+/fR1hYGNLT08U2Pz8/9OnTx+h/44mIqjqTx1TXrFkTWVlZSEtLe+65Fy5cQG5uLry9vU29HRERlRO5XI6srCwAgIODA8aMGYP+/fszUBMRlYLJofqFF14AAGzatOm5537++eeQyWQICAgw9XZERFROateujf79+6Nu3bqYMWMGmjZtKnVJRERWx+RQPXPmTAiCgPnz5xvMEH/W06dPMWvWLISHh4uvISIiaSUmJooTEfU6d+6MSZMmQaVSSVQVEZF1M3lMdUBAAF555RWsXLkSXbt2xaBBg5CdnQ0A+Prrr3Hp0iXs3LlTHB7y5ptvom3btmYpmoiISk8QBMTExODgwYPw9/dHnz59xGMymazQ5l1ERGQ8mSAIgqkv1mq1ePvtt/HDDz9Af5ln/1HW77A4e/ZsfP3115XuH+yMjAyoVCqkp6fDxcVF6nKIiIqVnZ2NyMhI3L59W2ybMmUK6tatK2FVRETlr6LyWplCtd7ly5exYsUKHD16FImJidBqtfD09IS/vz+mTZtWaXuoGaqJyBrEx8cjIiJCnIwIAD179kRAQADkcpNHARIRWQWrCtVVFUM1EVkynU6HI0eO4NChQ+JfE52cnBASEoIGDRpIXB0RUcWoqLzGPWeJiCqhrKwsbN68GXFxcWJbw4YNMWLECDg7O0tYGRFR5WTy3/369++P9evX4+nTp+ash4iIyigpKQk///yzGKhlMhl69+6NcePGMVATEZUTk0N1VFQUJk6cCE9PT0yaNAlRUVHmrIuIiEzk5uYm/omzWrVqmDBhAnr27Mnx00RE5cjkMdUvv/wytmzZguzsbHFVDy8vL4wfPx4vv/wyWrZsadZCLRHHVBORpUpJScH+/fsRHBwMJycnqcshIpKMVUxUfPr0KSIjI7F27VocOHAAWq1WDNjt2rXDxIkTMWbMGNSoUcNsBVsShmoisgS3bt2Ci4sLatasKXUpREQWxypC9bMePnyIX3/9FevXr8eFCxcKLi6TQaFQICgoCC+//DKGDRsGpVJpjttZBIZqIpKSVqvFwYMHcfToUdSoUQNTp06FnZ2d1GUREVkUqwvVz/rrr7+wdu1a/Pbbb7h//37BjWQyqFQqpKSkmPt2kmGoJiKppKenIyIiAgkJCWLbgAED0LVrVwmrIiKyPFYdqvUEQcCBAwcwZ84cnDlzBjKZDFqttrxuV+EYqolICtevX8fWrVuRk5MDAJDL5ejbty+6detW6XauJSIqK6tfp/rBgwfYsGED1q1bh0uXLpXXbYiIqgytVouoqCicOHFCbFOpVAgNDYW3t7eElRERkVlDdU5ODjZv3ixOXNTpdOIuXh06dMCECRPMeTsioiojNTUVERER4pA6AGjevDmGDh0KBwcHCSsjIiLATKE6KioK69atQ2RkJLKzs8Ug7e3tjXHjxmHChAlo0aKFOW5FRFTl5ObmYvny5eJwD4VCgX79+qFLly4c7kFEZCFMDtV//fUX1q1bhw0bNiAxMRFAwRhqZ2dnjBgxAhMmTEBgYCD/wSciKiN7e3t069YNBw8ehJubG0JDQ+Hl5SV1WURE9AyTQ3WbNm0gk8kgCALkcjkCAwMxYcIEjBw5Eo6OjuaskYioyuvRowdkMhk6d+4Me3t7qcshIqK/KdPwD19fX7z88ssYP348ateuba6aiIiqtMuXLyMzMxPdunUT22QyGXr06CFhVUREVBKTQ/XZs2fRvn17c9ZCRFSlqdVq7NmzB2fPnoVMJoOXlxfq1asndVlERGQEk0M1AzURkfkkJycjPDwcjx49AlAwR+Xq1asM1UREVqLc1qkmIiLjXLx4ETt27IBarQYA2NjYYODAgey8ICKyIkaF6k8//RQA4OHhgddee82grbQ++eQTk15HRFTZqNVq7N69G3/++afY5uHhgVGjRqFmzZoSVkZERKVl1DblcrkcMpkMzZo1w5UrVwzaSovblBMRAUlJSQgLC0NSUpLY1rZtWwQHB8POzk7CyoiIKheL2qa8Z8+ekMlkBmP79G1ERFQ6giBgy5YtYqC2tbVFcHAw2rVrJ21hRERkMqN6qqlo7KkmIlM9fvwYy5cvR/Xq1REaGooaNWpIXRIRUaVkUT3VRERUNoIgGPx1r2bNmhg/fjy8vLxga2srYWVERGQOclNfePjwYZw4ccLo80+dOoXDhw+bejsiIqskCALOnj2LNWvWQKPRGByrX78+AzURUSVh8vAPuVyO2rVr4/79+0ad36BBAyQkJBT6n4o14/APIipJXl4eduzYgb/++gsA0LVrVwwYMEDiqoiIqharGP5R2jzO4dtEVFU8ePAA4eHhSElJEdu0Wm2hYSBERFQ5VNiY6uzsbP6Zk4gqPUEQcObMGezZs0dcQlSpVGLIkCHw9fWVuDoiIiovFRKqr1+/juTkZHh7e1fE7YiIJJGbm4vt27eL6/kDQO3atREaGorq1atLWBkREZU3o0P11q1bsXXrVoO29PR0TJkypdjXCIKAtLQ0HDlyBDKZDD169DC9UiIiC5aYmIjw8HCkpqaKbV26dEG/fv1gY8OFloiIKjuj/6U/f/481qxZA5lMJo6NzsnJwZo1a4x6fY0aNTBv3jyTiiQisnRXr14VA7W9vT2GDRuG5s2bS1wVERFVFKNDdbt27TBx4kTx819++QUODg548cUXi32NXC6Hi4sLWrVqhZCQELi6upapWCIiS9WrVy/cuXMHOp0OoaGh/PeOiKiKKdOSep6enkhMTDR3TVaDS+oRVV1Pnz6Fo6OjQVt2djbs7e2hUCgkqoqIiP7O4pfUO3jwIOzs7MxZCxGRxRMEAcePH0d0dDQmT56M2rVri8ecnJwkrIyIiKRk8o6KAQEB8PPzM2ctz3X69GkEBwfDzc0NTk5O6NKlCzZs2GDy9dRqNdq1aweZTMaxj0T0XE+fPsVvv/2Gffv2Qa1WIywsDHl5eVKXRUREFsBqpqRHR0cjKCgIdnZ2GD16NFQqFTZv3oxx48YhPj4eH374YamvuXDhQty6dascqiWiyubu3buIiIhARkaG2NayZUuu7EFERACMHFMdGBgIAKhfvz5Wr15t0Faqm8lk2L9/f6lfp9Fo0Lx5c9y7dw/Hjx9H+/btAQCZmZnw8/PD9evXceXKFTRp0sToa547dw5du3bF4sWL8cYbb6BZs2a4du1aqerimGqiyk8QBBw9ehQHDhwQVz5ydHTEiBEj0LhxY4mrIyKi56movGZUqJbLC0aJNG/eXNzUQN9WqpvJZOIOY6Wxd+9eBAUFYfLkyVi1apXBsY0bN2L06NGYM2cOvvjiC6Oul5+fj06dOkGlUuHw4cOQy+UM1URUSHZ2NiIjI3H79m2xrX79+hg5ciR/5omIrIRFTVTUry/t4eFRqK0iREdHAwD69+9f6Ji+7dChQ0Zfb/78+bh58yYuXLgAmUxmlhqJqHK5e/cuwsLCkJWVJbb17NkTAQEBJnUqEBFR5VaqUP28tvJy8+ZNAChyeIebmxs8PDzEc57n9OnTWLRoEb744gs0bdq0VHXk5eUZTEp6dmwlEVUuCoUCT58+BVCwqsfIkSPRsGFDiasiIiJLZRXdLenp6QAAlUpV5HEXFxfxnJLk5eVh0qRJaN++Pd5+++1S1/Hll19CpVKJH3Xr1i31NYjIOtSpUwd9+/ZFgwYNMHPmTAZqIiIqkVWEanOZO3cubt68iVWrVpm0OcOcOXOQnp4ufiQkJJRDlUQkhXv37kGn0xm0devWDePHj4ezs7NEVRERkbUwOVTn5+fj7t27ePjwYaFjWVlZeOedd9C2bVt06NABc+fORU5OjslF6nuoi+uN1g9AL8m5c+ewePFifPTRR2jdurVJdSiVSri4uBh8EJF10+l0OHjwIFauXCnO39CTyWQcP01EREYx+f8WK1asQIMGDYpcH3rQoEH4z3/+g0uXLuH8+fP44osvMHDgQJi4I7o4lrqocdOpqalITk5+7nJ6Fy9ehFarxfz58yGTyQw+AOD69euQyWRwdXU1qUYisj6ZmZlYu3YtDh8+DAA4cuQI7t+/L3FVRERkjUzetWDPnj0AgLFjxxq0b9u2DUeOHIFcLsfYsWPh4OCAtWvX4siRI1i3bh0mTJhQ6nsFBATgyy+/xN69ezF69GiDY3v37hXPKUnTpk3xyiuvFHls5cqVUKlUCA0NhaOjY6nrIyLrc+vWLURGRoqTEWUyGQIDA+Hl5SVxZUREZI2MWqe6KE2bNsXt27eRnJwMNzc3sX306NEICwvDBx98gM8//xwA8PPPP+O1115D//798ccff5T6XhqNBs2aNcP9+/dx4sQJtGvXDoDh5i+XL18WV/NITk5GcnIyPDw8DJYBLI5MJuM61URVhE6nw4EDB3D06FGxzcXFBSEhIahXr56ElRERUXmoqLxm8vCPpKQkODo6GgRqADh48CAAYOrUqWLbyy+/DAC4cOGCSfeysbHBihUroNPp0KNHD0yfPl0cs3358mXMnz/fYHm8JUuWoEWLFliyZIlJ9yOiyik9PR1r1qwxCNRNmjTBjBkzGKiJiKhMTB7+kZ2dDQcHB4O2+Ph4JCUloV69emjQoIHY7uTkBFdXV6SkpJhcaO/evRETE4N58+Zh06ZNyM/Ph6+vLxYuXIhx48aZfF0iqhoePnyItWvXipOm5XI5+vTpAz8/P24CRUREZWZyqK5evTqSkpKQlpYmTu47cOAAAOCFF14odL5GoynzslRdunTB7t27n3ve/PnzMX/+fKOva+oESiKyHh4eHlCpVMjJyRHnUHh7e0tdFhERVRImD//o0KEDgIJJfkDBOMWVK1dCJpOhd+/eBucmJSUhKysLnp6eZSiViMh0NjY2CA0NRevWrTFjxgwGaiIiMiuTQ/WkSZMgCAI++OADDBw4EF26dMHx48fh7OyMUaNGGZx75MgRAECLFi3KVi0RkZGuXbuGpKQkgzZ3d3eMHDmy0NA1IiKisjI5VL/44ouYPHkytFot9uzZg3PnzsHe3h4///xzobWeN27cWGQPNhGRuWk0GuzevRsbN25EeHg41Gq11CUREVEVYPKYaqBg6MeUKVNw7NgxuLq6om/fvgYTFIGCnRdVKhUmTJiA4ODgMhVLRFSSlJQUhIeH48GDBwCAx48f48KFC+jUqZPElRERUWVn8jrVxHWqiSzJ5cuXsX37duTl5QEAFAoFgoKC0KlTJ67uQURUhVVUXitTTzURkdQ0Gg327NmDM2fOiG3Vq1fHqFGjODmaiIgqjFlCdX5+Pvbt24czZ87g8ePHkMlkqFGjBjp37oy+ffvCzs7OHLchIjLw5MkThIWF4dGjR2Jbq1atMHjwYCiVSgkrIyKiqqbMoXrZsmWYO3cukpOTizzu4eGBzz77DNOmTSvrrYiIRDk5OVi+fLk43MPGxgYDBw5E+/btOdyDiIgqXJlC9fvvv49vvvlG3DylTp064tqv9+7dw/3795GUlISZM2fi9u3b+Oqrr8peMRERAAcHB/j5+SE6OhoeHh4IDQ1FrVq1pC6LiIiqKJMnKh46dEhcIi8kJAQLFy5E8+bNDc65fv065s6di/DwcMhkMkRHR6NHjx5lr9pCcKIikbR0Oh2OHz+Ozp07c5gZEREVqaLymsnrVP/4448AgFdeeQVhYWGFAjUANGvWDJs2bcIrr7wCQRCwZMkS0ysloirt/PnzOHHihEGbXC6Hv78/AzUREUnO5J5qb29vPHz4EImJiahZs2aJ5z569AheXl6oXbs27t27Z1Khlog91UTlLz8/H7t27cKFCxcgk8kwefJk1K1bV+qyiIjISlj8knrJyclQqVTPDdQAUKtWLbi6uhY7mZGIqCiPHz9GWFiY+G+HIAi4efMmQzUREVkck0N1tWrVkJ6ejtzcXNjb25d4bk5ODjIzM9mbS0RGEQQBf/75J3bv3g2NRgMAsLOzw+DBg9G6dWuJqyMiIirM5DHVbdq0gVarxapVq5577qpVq6DRaNC2bVtTb0dEVUReXh4iIyOxfft2MVDXqlUL06dPZ6AmIiKLZXJP9bhx43Dw4EG8/fbbUCqVeOWVV4o8b8WKFXj77bchk8nw8ssvm1woEVV+Dx8+RFhYGFJSUsS2jh07YsCAAbCx4QawRERkuUyeqKjT6dCnTx8cOnQIMpkM3t7e6N27N+rUqQOZTIaEhAQcPHgQ9+/fhyAI6NWrF/bv31+pNmXgREUi8xEEAcuWLcPDhw8BFAz3GDp0KHx9fSWujIiIrFlF5TWTQzVQUOSUKVOwefPmgov9LTDrLx0SEoKVK1dWuuDJUE1kXo8ePcKKFStQo0YNhIaGonr16lKXREREVs4qQrXe6dOn8fvvv+PMmTN4/PgxAKBmzZro1KkTRo8ejc6dO5e5UEvEUE1UNoIgFPpl/O7du/Dy8uJwDyIiMgurCtVVFUM1kWkEQcCpU6dw5coVTJgwAQqFQuqSiIiokrLYdaqTkpKwZs0anD59GhkZGahevTq6deuGiRMnQqVSlUeNRFSJ5OTkYNu2bbh27RoAICoqCkFBQRJXRUREVDalCtW7d+/G6NGjkZWVZdC+ceNGfPbZZ9i6dSv8/PzMWiARVR737t1DeHg40tPTxTaZTFbkMBAiIiJrYvTwj4SEBPj6+oqBWi6Xw93dHcnJyeKExFq1auHKlStwc3Mrv4otCId/EBlHEAQcP34c+/fvh06nAwA4ODhg+PDhaNq0qcTVERFRZVZRec3ozV+WLFmCrKwsuLi4YMWKFcjOzsajR4+QmZmJRYsWQalU4vHjx1i9enW5FUtE1ufp06f4/fffsW/fPjFQ161bFzNmzGCgJiKiSsPoUB0VFQWZTIavv/4aU6ZMgVKpBAA4OjrinXfewQcffABBEBAVFVVuxRKRdbl79y6WLl2KGzduiG3+/v6cg0FERJWO0aE6NjYWADB27Ngij48fP97gPCKi69evIyMjA0DBL+Djxo1D3759udoHERFVOkZPVMzIyICHhwecnJyKPN6gQQMAKDSJkYiqrsDAQNy9excKhQIjR47k3AMiIqq0jA7VgiCU2Lsklxd0euvHTBJR1ZOdnW3wi7dCocCYMWNgb28v/htBRERUGfH/ckRUZjqdDocOHcJ3332Hhw8fGhxzdHRkoCYiokqvVOtUZ2Vl4dNPPy3TOZ988klpbklEFi4rKwubN29GXFwcACAsLAwzZsyAnZ2dxJURERFVHKPXqZbL5WbZnEGr1Zb5GpaC61RTVRcbG4vNmzcjOzsbQMFGLgEBAejRowd7p4mIyCJY5DblRuZvIqrk9MM9Dh8+LLY5OzsjJCQEPj4+0hVGREQkEaNDNScgEhEAZGZmIiIiAnfu3BHbGjVqhBEjRhS7OhAREVFlV6qeaiKq2uLi4hAeHo6nT58CKBjuERgYCH9/f7MMDyMiIrJWDNVEZDRbW1vk5uYCAFxcXBASEoJ69epJXBUREZH0GKqJyGje3t7o06cP4uPjMXz4cDg6OkpdEhERkUVgqCaiYt25cwd169Y1WMnDz88Pfn5+HO5BRET0DK55RUSFaLVa7N27F2vWrDFY4QMoGEfNQE1ERGSIPdVEZCAtLQ3h4eG4f/8+AODQoUNo3rw5PD09Ja6MiIjIcjFUE5Ho2rVr2Lp1qzgZUS6Xo3///qhVq5bElREREVk2hmoigkajwb59+3Dq1Cmxzc3NDaGhofDy8pKwMiIiIuvAUE1UxaWkpCA8PBwPHjwQ21q2bIkhQ4bA3t5ewsqIiIisB0M1URV2//59rFu3Dnl5eQAAhUKBoKAgdOrUiZMRiYiISsFsoVoQBDx58gRPnz7lZhBEVqJmzZpwdXXFo0ePUL16dYwaNYoTEomIiExQ5iX1zp07h5EjR0KlUqFWrVpo2LChwfHU1FTMmDEDM2fORH5+fllvR0RmZGtri9DQULRr1w7Tp09noCYiIjJRmUL1unXr4Ofnhy1btiArKwuCIEAQBINz3NzcEBcXh+XLl2Pfvn1lKpaIyubSpUtITk42aPPw8MCwYcOgVColqoqIiMj6mRyqr169imnTpkGtVuONN97AmTNn4OHhUeS5EyZMgCAI2Lp1q8mFEpHp1Go1tm3bhs2bNyM8PBxqtVrqkoiIiCoVk8dUL168GPn5+Zg1axa+/fZbAAWTnIoSGBgIADh+/LiptyMiEyUlJSE8PByPHz8GADx69AiXL19Gu3btpC2MiIioEjE5VB84cAAymQzvv//+c8/18vKCo6Mj7t69a+rtiMgE58+fx65du8SeaVtbWwQHBzNQExERmZnJoToxMRFOTk7w9vY26nwHBwekp6ebejsiKoX8/Hzs2rULFy5cENtq1KiBUaNGoUaNGhJWRkREVDmZHKqVSiVyc3MhCMJz17PNyclBWloaXF1dTb0dERnp8ePHCAsLM5iQ2L59ewwcOBC2trYSVkZERFR5mTxR0cfHB2q1Gjdv3nzuubt27YJWq0XLli1NvR0RGSE7OxsrVqwQA7WtrS1GjBiBoUOHMlATERGVI5ND9YABAyAIAr777rsSz3vy5Anee+89yGQyDBo0yNTbEZERnJyc4OfnBwCoVasWpk+fjjZt2khcFRERUeUnE/6+sLSRHj16hCZNmiA7OxuffPIJ3nrrLTRt2hSPHz+GVqtFTk4OIiMj8dFHH+HOnTvw8PDArVu34OLiYu73IJmMjAyoVCqkp6dXqvdF1k2n0+HkyZPo1KkTe6eJiKjKq6i8ZnKoBoAdO3YgNDQUarUatra20Ol00Gq1aN68OWJjY5Gfnw9BEKBUKrFjxw706dPHnLVLjqGapCQIAs6ePQutVouuXbtKXQ4REZFFqqi8VqYdFQcPHozDhw+jY8eOyM/Ph0ajgSAIuHr1KvLy8iAIAtq3b4/Dhw9XukBNJKXc3FxERERg586d2Lt3L+7duyd1SURERFWayat/6HXp0gWnTp3CxYsXERMTg8TERGi1Wnh6esLf3x+dOnUyR51E9D+JiYkIDw9HamoqgILhHrGxsUYvb0lERETmV+ZQrdemTRtOiCIqR4Ig4NSpU9i3bx+0Wi2AgqUthw0bhhYtWkhcHRERUdVmtlBNROUnJycH27Ztw7Vr18S2OnXqICQkBG5ubhJWRkRERABDNZHFu3fvHiIiIpCWlia2+fn5oU+fPlAoFNIVRkRERCKTQ3VgYGCpXyOTybB//35Tb0lU5QiCgG3btomB2sHBAcOGDUOzZs2kLYyIiIgMmLyknlxu3MIh+i3M9duZ68eCVgZcUo8qwsOHD7FixQp4eXkhJCQEKpVK6pKIiIisRkXlNZN7qufNm1fi8fT0dJw8eRLHjx+Hu7s7Xn31Vf6pmsgIOp3O4JdWT09PTJw4EV5eXvwZIiIislBl2vzFGAcOHMDIkSPRt29fhIeHl+etKhx7qsmcBEHA0aNHcfPmTUyYMIEBmoiIyAysYvMXYwQGBuK7775DZGQkVqxYUd63I7JK2dnZ2LBhA/bv34+7d+/iwIEDUpdEREREpVDuoRoAXnrpJSgUCoZqoiLcuXMHS5cuxa1bt8Q2GxsblPMfkYiIiMiMKmRJPXt7ezg5OeHq1asVcTsiq6DT6RATE4Po6GgxQDs5OWHEiBFo1KiRxNURERFRaVRIqL5//z7S09Ph7OxcEbcjsnhZWVmIjIxEbGys2NagQQOMGDEC1apVk7AyIiIiMkW5h+qcnBy89tprAIDWrVuX9+2ILF5cXBwiIiKQnZ0NoGDZyYCAAPTo0cPopSqJiIjIspgcqj/99NMSj+fm5iIhIQF79uzBkydPIJPJMGvWLFNvR1Rp3LhxQwzUzs7OCAkJgY+Pj7RFERERUZmYHKrnz58vbuxSEkEQIJfL8dFHH2Hs2LGm3o6o0ujbty/u3r0LBwcHjBgxAk5OTlKXRERERGVkcqju2bNniaHaxsYGbm5uaNu2LV588UU0adLE1FsRWbWsrCyD+QQKhQLjxo2Dg4ODUb+YEhERkeUzOVRHR0ebsQyiyken0+HgwYM4efIkXnnlFdSqVUs85ujoKGFlREREZG6cFUVUDjIyMvDLL78gJiYGarUaYWFhyM/Pl7osIiIiKicm91TL5XLI5XJcu3YNjRs3NmdNRFbt5s2biIyMRE5ODoCCn5UOHTrA1tZW4sqIiIiovJgcqh0cHGBra8tATfQ/Wq0WBw4cwLFjx8Q2lUqFkJAQ1K1bV8LKiIiIqLyZHKq9vb1x7949c9ZCZLXS0tIQERFh8DPRrFkzDBs2DA4ODhJWRkRERBXB5DHVgwYNQm5uLg4dOmTOeoiszs2bN7F06VIxUMvlcgQFBeGll15ioCYiIqoiTA7Vc+bMQY0aNfDqq6/iwYMH5qypWKdPn0ZwcDDc3Nzg5OSELl26YMOGDUa/PiYmBm+//TY6duwId3d32Nvbo3nz5nj//feRlpZWfoVTpWZvb4+8vDwAgKurK6ZMmYJu3bpxuTwiIqIqRCYIgmDKCw8fPoybN29i9uzZUCgUePnll+Hv74+aNWtCoVAU+7qePXuaVGh0dDSCgoJgZ2eH0aNHQ6VSYfPmzYiLi8Pnn3+ODz/88LnX8PT0RHJyMrp374727dtDJpMhOjoaf/75Jxo1aoRjx46hZs2aRteUkZEBlUqF9PR0uLi4mPS+qHKIiYlBYmIihg4dCnt7e6nLISIiov+pqLxmdKheu3YtHBwcMGrUKAAFf+IubU+cTCaDRqMpdZEajQbNmzfHvXv3cPz4cbRv3x4AkJmZCT8/P1y/fh1Xrlx57gYz//rXvzBhwgTUrl1bbBMEAbNmzcJPP/2E1157DT/++KPRdTFUV01xcXGoX78+5PL//0OP/seIvdNERESWpaLymtHDPyZNmoQ333zToE0QhFJ96HQ6k4o8cOAAbt++jbFjx4qBGgCqVauGuXPnQqPRYPXq1c+9zvvvv28QqIGCEDR37lwA4PhwKpFGo8GuXbuwdu1axMTEGByTyWQM1ERERFVYqVb/eLZT29SAbAr97o39+/cvdEzfVpZArF8/2Mam5C9HXl6eOHYWKPjNh6qGJ0+eIDw8HA8fPgRQ8D3ZvHnzUg0XIiIiosrLKnZUvHnzJgAUObzDzc0NHh4e4jmmWLVqFYCiQ/uzvvzyS6hUKvGDaw9XDX/99ReWLVsmBmobGxsMGjQINWrUkLgyIiIishRWEarT09MBFGykURQXFxfxnNI6f/48FixYgJo1a+K9994r8dw5c+YgPT1d/EhISDDpnmQd1Go1tm/fjoiICHGLcXd3d0ydOhUdO3bkcA8iIiISmbz5S2UQFxeHwYMHQ6vV4vfff4eHh0eJ5yuVSiiVygqqjqSUnJyMsLAwPH78WGxr06YNBg0aBDs7OwkrIyIiIktkFaFa30NdXG+0flZnady5cwe9e/dGUlISIiIi0Lt37zLXSZVDQkIC1q1bB7VaDeD/h3u0a9dO2sKIiIjIYpVq+MejR4+gUChM/njeRMDi6MdSFzVuOjU1FcnJyc9dTu9Z8fHx6NWrFxITE7Fp0yYMHjzYpLqocvL09ISbmxsAoEaNGpg+fToDNREREZWo1GOqS7uM3t8/TBEQEAAA2Lt3b6Fj+jb9Oc+jD9T379/Hxo0bMWzYMJNqosrL1tYWoaGh6NSpE6ZNm8YJiURERPRcRm/+IpfL4ezsjLfffrtMN5w3b16pX6PRaNCsWTPcv38fJ06cEHsNn9385fLly2jatCmAgvGwycnJ8PDwMBgn/fdAPXLkyDK9F27+Yv0EQcD58+dRr149uLu7S10OERERmZnF7agol8vh6emJxMTEciumJAcPHkRQUBCUSiXGjBkDFxcXcZvyzz77DB999JF47vz587FgwQLMmzcP8+fPF9t9fHxw584ddOvWDUFBQUXe59nzn4eh2rrl5+djx44duHTpEjw9PfHKK6+YPESJiIiILFNF5TWrSRC9e/dGTEwM5s2bh02bNiE/Px++vr5YuHAhxo0bZ9Q17ty5AwA4ceIETpw4UeQ5pQnVZL0ePnyI8PBwPHnyRPz82rVraNWqlcSVERERkTWymp5qS8SeausjCALOnj2LP/74A1qtFgBgZ2eHIUOGMFATERFVQuypJjKzvLw8bN++HZcvXxbbateujdDQUFSvXl3CyoiIiMjaMVRTlfDgwQOEhYUhNTVVbOvSpQv69evHcdRERERUZkwTVOllZmZi1apV0Gg0AAp2xhw2bBhatGghcWVERERUWRgdqnU6XXnWQVRuqlWrBj8/Pxw5cgReXl4IDQ0VN3chIiIiMgf2VFOV0KtXLzg5OaFTp05QKBRSl0NERESVDEM1VSqCIODEiRNQKBTo0qWL2C6Xy9G1a1cJKyMiIqLKjKGaKo2cnBxs2bIFN27cgFwuh7e3N7y8vKQui4iIiKoAhmqqFBISEhAeHo6MjAwABXMA7ty5w1BNREREFYKhmqyaIAg4duwY9u/fD/0+Ro6Ojhg+fDiaNGkicXVERERUVTBUk9XKzs7Gli1bcOvWLbGtXr16CAkJ4Q6XREREVKEYqskq3blzBxEREcjMzBTbevTogV69ekEul0tYGREREVVFDNVkdXQ6HbZv3y4GaicnJ4wYMQKNGjWSuDIiIiKqqtilR1ZHLpdj5MiRUCgU8PHxwYwZMxioiYiISFLsqSaroNPpDIZ1eHl5YdKkSfDy8uJwDyIiIpIc0whZNJ1Oh+joaKxduxY6nc7gmLe3NwM1ERERWQT2VJPFyszMxObNmxEfHw8AOHjwIPr06SNtUURERERFYKgmi3T79m1s3rwZT58+BQDIZDLY2dlJXBURERFR0RiqyaLodDocPHgQMTExYlu1atUQEhKC+vXrS1gZERERUfEYqsliZGRkICIiAnfv3hXbGjdujBEjRsDR0VHCyoiIiIhKxlBNFuHmzZuIjIxETk4OgIJl8wIDA/HCCy9AJpNJXB0RERFRyRiqySLcunVLDNQqlQohISGoW7euxFURERERGYehmixCv379kJCQABcXFwwbNgwODg5Sl0RERERkNIZqkkRGRgZcXFzEz21sbPDyyy/D3t6ewz2IiIjI6nDnDKpQWq0Wf/zxB5YsWYLHjx8bHHNwcGCgJiIiIqvEUE0VJjU1FatWrcLJkyehVqsRHh4OtVotdVlEREREZcbhH1Qhrly5gm3btiEvLw8AoFAo0KlTJ9jY8FuQiIiIrB8TDZUrjUaDvXv34vTp02Kbm5sbRo0ahdq1a0tYGREREZH5MFRTuUlJSUFYWBgePnwotvn6+mLIkCFQKpUSVkZERERkXgzVVC6uXbuGyMhI5OfnAygY7jFw4EB06NCBkxGJiIio0mGopnLh4OAgTkJ0d3fHqFGjUKtWLYmrIiIiIiofDNVULurXr49evXrhyZMnGDRoEOzs7KQuiYiIiKjcMFSTWdy+fRsNGzY0GNrRo0cPAOBwDyIiIqr0uE41lYlarcbWrVuxfv16xMTEGByTyWQM1ERERFQlsKeaTPb48WOEh4cjKSkJAHDw4EG0bNkS7u7uEldGREREVLEYqqnUBEHA+fPnsWvXLmg0GgCAra0tBg0axEBNREREVRJDNZVKfn4+du7ciYsXL4ptNWvWxKhRo+Dh4SFhZURERETSYagmoz169AhhYWF48uSJ2NaxY0cEBQXB1tZWwsqIiIiIpMVQTUaJj4/Hr7/+Kg73sLOzw5AhQ9CqVSuJKyMiIiKSHkM1GcXLywuurq5ITk6Gp6cnQkNDOX6aiIiI6H8YqskodnZ2GDVqFM6dO4e+ffvCxobfOkRERER6XKeaChEEAWfOnEFKSopBe82aNTFgwAAGaiIiIqK/YToiA7m5udi+fTuuXLmC2rVrY8qUKQzRRERERM/BtESi+/fvIzw8HGlpaQCABw8e4ObNm2jRooW0hRERERFZOIZqgiAIOHnyJPbt2wedTgcAsLe3x7Bhw9C8eXOJqyMiIiKyfAzVVVxOTg62bt2K69evi23e3t4ICQmBq6urdIURERERWRGG6iosISEBERERSE9PF9teeOEFBAYGQqFQSFgZERERkXVhqK6i0tPTsWbNGnG4h4ODA4YPH46mTZtKXBkRERGR9eGSelWUSqWCn58fAKBevXqYOXMmAzURERGRidhTXYX17t0bKpUKHTt2hFzO36+IiIiITMUkVQUIgoAjR47g9OnTBu0KhQKdO3dmoCYiIiIqI/ZUV3LZ2dmIjIzE7du3oVAo4O3tjdq1a0tdFhEREVGlwlBdicXHxyMiIgJZWVkAAK1Wi4SEBIZqIiIiIjNjqK6EdDodDh8+jMOHD0MQBACAs7MzRo4ciQYNGkhcHREREVHlw1BdyWRmZiIyMhJxcXFiW8OGDTFixAg4OztLWBkRERFR5cVQXYncvn0bkZGRyM7OBgDIZDL06tULPXr0gEwmk7g6IiIiosqLobqS0Gq12Llzpxioq1WrhpCQENSvX1/iyoiIiIgqP66lVkkoFAqEhIRALpejcePGmDFjBgM1ERERUQVhT7UV02q1UCgU4ud16tTBK6+8gtq1a3O4BxEREVEFYk+1FdJqtYiKisL69euh0+kMjnl5eTFQExEREVUw9lRbmfT0dERERCAhIQEAEB0djcDAQImrIiIiIqraGKqtyPXr17Flyxbk5uYCAORyORwdHSWuioiIiIgYqq2AfrjHiRMnxDZXV1eEhoaiTp06ElZGRERERABDtcVLTU1FREQE7t+/L7Y1b94cw4YNg729vYSVEREREZEeQ7UFu3r1KrZu3Yq8vDwABcvm9e/fH507d+ZkRCIiIiILwlBtwWJjY8VA7ebmhtDQUHh5eUlcFRERERH9HUO1BQsKCsK9e/fg7u6OIUOGQKlUSl0SERERERWBodqCpKenQ6VSiZ/b2Nhg4sSJUCqVHO5BREREZMG4+YsFUKvV2LFjB3788UckJycbHLO3t2egJiIiIrJwDNUSS05OxsqVK3H27Fmo1WqEhYVBo9FIXRYRERERlQKHf0jo4sWL2LFjB9RqNYCC4R7dunWDQqGQuDIiIiIiKg2Gagmo1Wrs3r0bf/75p9jm4eGBUaNGoWbNmhJWRkRERESmYKiuYElJSQgLC0NSUpLY1q5dOwwcOBB2dnYSVkZEREREpmKorkCXL1/G1q1bxeEetra2GDRoENq2bStxZURERERUFgzVFcjJyUmchFizZk2MGjUKHh4eEldFRERERGXFUF2BfHx8EBAQgIyMDAwYMAC2trZSl0REREREZsBQXU4EQcDNmzfRpEkTg3Wme/bsyXWniYiIiCoZrlNdDvLy8rB582b89ttvOHbsmMExBmoiIiKiyseqQvXp06cRHBwMNzc3ODk5oUuXLtiwYUOprqHT6bBkyRK0adMGDg4OqFGjBl588UXcvHnTLDU+ePAAy5Ytw19//QUAOHDgAFJTU81ybSIiIiKyTFYz/CM6OhpBQUGws7PD6NGjoVKpsHnzZowbNw7x8fH48MMPjbrOzJkzsXz5crRs2RKvv/46Hj16hI0bN2Lv3r04duwYWrZsaVJ9giDgzJkz2LNnD7RaLQBAqVRi6NChcHNzM+maRERERGQdZIIgCFIX8TwajQbNmzfHvXv3cPz4cbRv3x4AkJmZCT8/P1y/fh1XrlxBkyZNSrzOwYMHERgYiB49emDfvn1QKpUAgP3796Nfv37o0aMHDh06ZHRdGRkZUKlUePToEQ4dOoQrV66Ix7y8vBAaGspATURERCQhfV5LT0+Hi4tLud3HKoZ/HDhwALdv38bYsWPFQA0A1apVw9y5c6HRaLB69ernXmf58uUAgM8++0wM1ADQp08fBAUF4fDhw7hx40ap61u9erVBoO7atSsmT57MQE1ERERURVhFqI6OjgYA9O/fv9AxfZsxPczR0dFwcnKCv79/oWNBQUFGX+fv0tLSAAD29vZ46aWXMGDAANjYWM3IGiIiIiIqI6tIfvpJhEUN73Bzc4OHh8dzJxpmZ2fjwYMHaNWqFRQKRaHj+muXdJ28vDzk5eWJn6enp4vtXl5eGDZsGFxdXZGRkfH8N0VERERE5U6fy8p7xLNVhGp9eFWpVEUed3Fxwb1798p8jWfPK8qXX36JBQsWFGr/z3/+AwB44403SqyBiIiIiKTx5MmTYnOgOVhFqLYUc+bMwVtvvSV+npaWhvr16+Pu3bvl+pDIMmRkZKBu3bpISEgo14kOZBn4vKsWPu+qhc+7aklPT0e9evVQvXr1cr2PVYRqfWAtrhdZP6uzrNd49ryiKJVKgwmOz16bP5RVh4uLC593FcLnXbXweVctfN5Vi1xevlMJrWKiYknjnVNTU5GcnPzc5fScnJxQu3ZtxMXFietIP6ukcdtERERERCWxilAdEBAAANi7d2+hY/o2/TnPu052djaOHj1a6NiePXuMvg4RERER0bOsIlT36dMHDRs2xIYNG3D+/HmxPTMzEwsXLoSNjQ0mTZokticnJ+PatWtITk42uM706dMBAB9//DHy8/PF9v3792PPnj3o2bMnmjZtanRdSqUS8+bNK3JICFU+fN5VC5931cLnXbXweVctFfW8rWJHRaBgN8SgoCAolUqMGTMGLi4u2Lx5M+Li4vDZZ5/ho48+Es+dP38+FixYgHnz5mH+/PkG15k2bRpWrFiBli1bYtCgQeI25fb29mXappyIiIiIqi6r6KkGgN69eyMmJgbdu3fHpk2b8N///hfu7u5Yv369QaB+nqVLl+L777+HTCbD999/j507d2LIkCE4deoUAzURERERmcRqeqqJiIiIiCyV1fRUExERERFZKoZqIiIiIqIyYqj+m9OnTyM4OBhubm5wcnJCly5dsGHDhlJdQ6fTYcmSJWjTpg0cHBxQo0YNvPjii0Wus03SKuvzjomJwdtvv42OHTvC3d0d9vb2aN68Od5//32kpaWVX+FkEnP8fD9LrVajXbt2kMlkaN68uRkrJXMw1/POzMzEvHnz0KpVKzg6OsLV1RUdOnTAggULyqFqMpU5nndaWho++eQTtGnTBtWqVYOHhwc6d+6MJUuWIDc3t5wqp9Jav349ZsyYgU6dOkGpVEImk2HNmjWlvo7Z85pAooMHDwp2dnaCs7OzMHXqVOHtt98WGjRoIAAQPv/8c6OvM23aNAGA0LJlS+Hdd98VJkyYICiVSkGlUgmXL18ux3dApWGO512rVi1BoVAIAQEBwptvvinMnj1baN++vQBAaNSokfDo0aNyfhdkLHP9fD9r7ty5gpOTkwBAaNasmZkrprIw1/O+c+eO0KhRI0Emkwn9+vUT3nvvPeGf//ynMGjQIKF169bl+A6oNMzxvFNTU4WGDRsKAITu3bsLb7/9tvCPf/xDaNSokQBACAwMFLRabTm/EzJG/fr1BQCCh4eH+N+rV68u9XXMndcYqv9HrVYLjRo1EpRKpXDu3DmxPSMjQ/D19RVsbGyEGzduPPc6Bw4cEAAIPXr0EHJzc8X2qKgoQSaTCT179iyX+ql0zPW8v/rqKyExMdGgTafTCa+++qoAQHjttdfMXjuVnrme97POnj0r2NjYCN9//z1DtYUx1/PWaDRC586dBQcHB+HAgQNF3oekZ67n/a9//UsAIMyePdugPS8vT+jcubMAQDh06JDZ66fS27dvnxAfHy8IgiB8+eWXJoXq8shrDNX/s2fPHgGAMHny5ELHfv/9dwGAMGfOnOdeZ8yYMcX+4A0YMEAAIFy/ft0sNZPpzPW8i5OYmCgAEHx9fctSJpmJuZ93Xl6e0Lp1a6F79+6CTqdjqLYw5nre+nPnzp1bHmWSmZjrec+YMUMAIOzbt6/QsQ8//FAAIISFhZmlZjIfU0N1eeQ1jqn+n+joaABA//79Cx3Ttx06dMio6zg5OcHf37/QsaCgIKOvQ+XLXM+7OLa2tgAAGxsbk69B5mPu5z1//nzcvHkTK1euhEwmM0uNZD7met4bN24EAIwaNQoJCQn4+eef8dVXXyEsLAxZWVnmK5jKxFzP29fXFwDwxx9/GLSr1WpERUXBwcEBfn5+ZayWLEV55DX+H/9/9IPSmzRpUuiYm5sbPDw8njtwPTs7Gw8ePECrVq2gUCgKHddfmxMWpWeO512SVatWASj6H3mqeOZ83qdPn8aiRYvwxRdfoGnTpmatk8zDXM/7zJkzAAomJM+ePRt5eXnisRo1amDTpk3o1auXeYomk5nreU+dOhXr1q3Dv//9b5w5cwadO3dGXl4e/vjjD6SmpmLDhg2oU6eO2eunildeeY091f+Tnp4OAFCpVEUed3FxEc8pyzWePY+kY47nXZzz589jwYIFqFmzJt577z2TayTzMdfzzsvLw6RJk9C+fXu8/fbbZq2RzMdcz/vx48cAgNdffx1vvvkmEhISkJSUhO+//x7p6ekYPnw4Hjx4YL7CySTmet4ODg6Ijo7G+PHjcejQIXzzzTf44YcfcPv2bYwdOxbdu3c3a90knfLKawzVRGYUFxeHwYMHQ6vV4vfff4eHh4fUJZEZzZ07Fzdv3sSqVauK7N2gykWn0wEABg8ejK+++gre3t7w8PDA66+/jtmzZyM9PR0rV66UuEoyl+TkZPTr1w8nTpzAzp07kZaWhocPH+Lnn3/G6tWr0bVrV6SmpkpdJlkwhur/0f+2UtxvJRkZGcX+RlOaazx7HknHHM/77+7cuYPevXsjKSkJ4eHh6N27d5nrJPMwx/M+d+4cFi9ejI8++gitW7c2e41kPub6+dafM3To0ELHhgwZAuD/h4iQdMz1vN966y0cO3YMERERCA4OhkqlQq1atTBt2jQsWrQIsbGx+Pbbb81ZOkmkvPIaQ/X/lDR+JjU1FcnJyUWO13qWk5MTateujbi4OGi12kLHSxr3RRXLHM/7WfHx8ejVqxcSExOxadMmDB482Gy1UtmZ43lfvHgRWq0W8+fPh0wmM/gAgOvXr0Mmk8HV1dXs9VPpmOvnu1mzZgBQ5DPVt+Xk5JheKJmFuZ73zp07Ub16dbRp06bQscDAQADA2bNny1gtWYLyymsM1f8TEBAAANi7d2+hY/o2/TnPu052djaOHj1a6NiePXuMvg6VL3M9b+D/A/X9+/exceNGDBs2zHyFklmY43k3bdoUr7zySpEfQEGPxiuvvIIJEyaYuXoqLXP9fOuD1JUrVwod07f5+PiYWiaZibmed35+PjIyMpCfn1/oWFJSEgBAqVSWpVSyIOWS10q1AF8lplarhYYNGwpKpVL4888/xfZnF49/dr3CpKQk4erVq0JSUpLBdZ5dTDwvL09s5+YvlsVczzsuLk6oX7++YGNjI0RERFRU+VRK5nrexQHXqbYo5nresbGxglKpFGrWrCncu3fP4Drt2rUTAAhRUVHl/n6oZOZ63kFBQQIA4eOPPzZoz83NFY/98MMP5fpeqPSet051ReY1hupnHDhwQLC1tRWcnZ2FadOmGWxz+tlnnxmcO2/ePAGAMG/evELXmTp1KrcptwLmeN767VG7desmzJs3r8gPsgzm+vkuCkO15THX89bvmOnu7i5MnTpVmDVrluDj4yMAEKZPn15B74aexxzP+88//xSqVasmABC6dOkizJ49W3j11VfFrcs7duwo5OTkVOC7ouIsX75cmDhxojBx4kShQ4cOAgDB399fbIuMjBTPrci8xlD9NydPnhQGDBggqFQqwcHBQejUqZOwfv36QueV9JC0Wq3w/fffC76+voJSqRTc3d2F0NBQ7qRogcr6vAE894Mshzl+vovCUG2ZzPW8t23bJvTo0UNwdnYW7O3thY4dOwrLli0r5+qptMzxvG/cuCFMnjxZqFevnmBrays4ODgIrVu3FhYsWCBkZ2dXwLsgY0ycOLHE/+8++2wrMq/JBEEQSjdghIiIiIiInsWJikREREREZcRQTURERERURgzVRERERERlxFBNRERERFRGDNVERERERGXEUE1EREREVEYM1UREREREZcRQTURERERURgzVRERERERlxFBNRCWKj4+HTCaDTCZDfHy81OVUKj4+PpDJZFizZo1Jr+ezqRxWrFgBmUyG1157TepSzEan08HX1xe2tra4fv261OUQVQiGaiIrNH/+fDFMPe+jqlmzZk2RXwc7Ozt4enqif//+WLFiBdRqtdSllmj+/PmYP39+pQzLvXr1KvIZOTk5oVGjRhg9ejT27NlTbvf/9ttvMX/+fJw/f77c7mGs7OxszJ07F0qlEh9++GGh45MmTTLq59zHx8fgdc/+wvXsh0KhQPXq1eHn54dPP/0UycnJRdZV1GvlcjlcXFzQpk0bzJo1C1euXCn2fcnlcsydOxcajQbvvfdemb5GRNbCRuoCiKhsatWqJXUJFsvDwwMKhQIAkJWVhUePHmHfvn3Yt28fli5dir1798LNzU2y+ho1agR7e3uoVKpCxxYsWACgIID+PTDp2draolmzZuJ/WxtbW1tUr15d/PzJkyeIjY1FbGwsNm7ciKlTp2LZsmVm/+Xw22+/xZ07d+Dj44N27dqZ9dqltWjRIjx8+BCzZs2Ct7d3sefJ5XLUqFGj2OMlHXNxcYGDgwMAID8/H6mpqThx4gROnDiBH3/8ETt37kSnTp2KfK2TkxOcnZ0BAFqtFk+ePMGlS5dw6dIlLF++HD///DOmTJlS5GtffPFFLFy4ENu2bcPhw4fRs2fPYmskqgzYU01k5R4+fFjiR1V2+vRp8euQlZWF2NhYjB07FgBw5swZTJ8+XdL69u/fj2vXrmHEiBEmvb5OnTq4du0arl27hjp16pi5uvL3wgsvGHyv5ubm4syZM+jRoweAgmERq1atkrjK8pOTk4MffvgBADBz5swSz61bt26JP+enT58u9rXfffedeF5KSgpSUlLw2WefwdbWFo8fP8bIkSORm5tb5Gvfeecd8bVJSUnIycnBli1bULduXajVasyYMaPY4R1yuRzTpk0DUPDLA1Flx1BNRFVGgwYNsH79ejG0RUREVPlfPCyJQqFAx44dsXXrVri7uwMAVq5cKXFV5Wfjxo1ITU1Fu3bt0KpVqwq7r5ubGz766CO8//77AICEhARs3brVqNcqlUoMGzYMv/76KwBAo9Hgl19+Kfb8MWPGQKFQYPfu3bh7927ZiyeyYAzVRFWAWq3Gvn378MYbb6BTp06oXbs27OzsULNmTQQFBeG3336DIAgmXfvevXuYPXs2fH194eTkBKVSCS8vL3Ts2BGzZ88usQctOjoaY8aMQb169cRhEF26dMGiRYuQnZ1t6tstkUwmw/jx4wEAgiDgzJkzBscfPnyId999F76+vnB2doaTkxN8fX3x3nvv4dGjR8VeNzU1FZ988gk6dOgAFxcXcQx3mzZtMHPmTOzfv7/Qa4qaqKgfQ6vXu3fvYsfOFjdR8Y033oBMJkOHDh1K/FpkZWXByckJMpkM69evL3Q8NzcX33//PQICAuDh4SG+p+HDh+OPP/4o8dpl4ebmhq5duwIALl++XOQ5169fx9dff42+ffuiUaNGcHBwgIuLC9q3b4+PP/64yLHC+rkId+7cAQBMnjzZqDkI5fV9unz5cgAQ/3pS0V5++WXxv0v6OS1K9+7d4eTkBKD4ZwQUDE8LDAyETqer1L8gEQEABCKyOvPmzRMACMb+CB88eFA8H4CgVCoFZ2dng7ZRo0YJWq220Gvj4uLEc+Li4gyOnT9/XnBzcxOPKxQKwc3NTZDJZGLbxIkTC11TrVYLU6dONbi/s7OzoFAoxM+bNWsmxMfHl/prs3r16mLr1du5c6d4zq+//iq2R0dHC66uruIxR0dHwcnJSfzczc1NOHLkSKHrJSQkCPXq1RPPk8vlgpubm8H7CQgIKPS6+vXrCwCE1atXi21vvPGGUKtWLYN71qpVS/zo1KmTeG5xz+b06dNi+19//VXs12rNmjXi1z4rK8vg2I0bN4QmTZqI15HJZIJKpTJ4Zq+++mqx1y5JQEBAsV8TvYEDBwoABCcnpyKP6792+tpcXV0Nvu/q1KkjXLt2zeA1X3/9tVCrVi1BLpcLAAQXFxeDr22tWrUMzi/P79O0tDSxjuPHjxd73sSJEwUAQv369Ut1/We/N579/npWdna2eM60adMMjunb582bV+RrdTqd+LMxaNCgEmtZuHChAEDo0qVLqd4DkbVhTzVRFeDg4ICxY8di586dePjwIXJycpCZmYknT57gu+++g4uLC8LCwrBkyZJSXfftt99GamoqOnTogOPHj0OtViMlJQW5ubm4ceMGvvnmG/j6+hZ63TvvvIMVK1agVq1a+O9//4snT54gMzMTOTk5OHjwINq3b4/r169j5MiR0Ol05voyiJ7t1dVPlEtISMDw4cORlpaGli1bIiYmBtnZ2cjKysLhw4fRrFkzpKamYtiwYbh//77B9ebPn4+7d+/Cx8cHUVFRyM/PR0pKCvLy8hAfH4+ffvoJ3bp1M6o2/fhXvc2bNxs9dlavU6dOaNmyJQBg3bp1xZ6nPzZy5Eix1xEA0tLS0L9/f9y8eROBgYE4fPgwcnJykJaWhrS0NCxevBjOzs746aef8N133xn1vkojNTUVp06dAgA0bNiwyHO6deuGH374Abdu3UJubi5SU1ORm5uLqKgodOnSBffv3y/UA6wfH1y3bl0AhmONi5qDUJ7fpzExMdDpdLC1tZVssmRRPwfGOnLkiNhLX9wz0tP/1eHcuXPIysoqXZFE1kTqVE9EpfdsT/Xfe9qe/Sipl/JZYWFhAgChUaNGhY6V1FPt4OAgABCOHTtmdO2XLl0SZDKZ4OjoKFy8eLHIczIyMgRvb28BgBAZGWn0tQXh+T3VarVaaNu2rdijnJycLAiCIMycOVPsGX7w4EGh1yUkJAguLi4CAGHWrFkGx1q0aCEAEDZs2FCqWovqqdbTv4eDBw8W+/qSns2XX34pABC8vb2L/AvEvXv3xJ7SqKgog2PvvPOOAEAIDAwU1Gp1kffevHmzAEDw8PAo9pziFNdTrdFohDNnzgg9evQQ39fixYtLdW1BEITMzEyxt7+ovyyU9HXXK+/v07lz5woAhFatWpV4nr6nWi6Xl/iznp6ebvA6Y3qqZ82aJZ7z9/r17X/vqc7NzRW2bNki1K1bVzzn7NmzJb6HpKQk8dwDBw6UeC6RNWNPNZGVe/ToUbEfxq7FPGjQIADA7du38eDBA6Pv7erqCgCles3KlSshCAIGDRqE1q1bF3lOtWrVMHz4cAAw23rFWVlZOHHiBIKDg3HhwgUAwMSJE+Hu7g5BELBp0yYABasweHp6Fnq9t7e3uELD77//bnDMlK9DeRs/fjzkcjnu3buHgwcPFjr+66+/QqfTwdvbG7179xbbBUEQV9x4++23YWNT9Mqrw4cPh4uLC5KTk3H27FmTajx27Bg8PT3FD3t7e3Tq1AlHjhwBAISEhOAf//hHqa/r7OyMgIAAAAU9wqYo7+/TxMREACUvhfcsnU5X4s+6sT3l+fn5uHr1Kt544w389NNPAIAmTZpg8ODBRZ7/zTffiM+nRo0acHBwwPDhw5GQkCAef97Y/erVq0Mulxu8b6LKiOtUE1k5wcgJhpmZmfj555+xY8cOXL16FWlpaUWG7vv376N27dpGXXPw4MFYvnw5Jk6ciKNHj2Lo0KHo3LkzHB0di32NPuTs3r27yPCqp/8zsX5SmSkaNGhQ7LG+ffuKy5nFxcUhJSVFbC9Ov379sGjRIjx58gRxcXHi9QcPHozjx4/jgw8+wLVr1zBy5Ei88MILcHFxMbn2svL29kavXr1w4MABrFu3Dn369DE4rh/6MW7cODHwAMCVK1fEr8WkSZMMjv3ds89I/yf+0lCr1UVO/pTJZFiyZMlzdxjcsWMH1q1bh9OnT+PRo0d4+vRpoXPu3btX6rqA8v8+TUpKAmD8sIv69eubvBHQ5MmTMXny5CKPNWjQANu2bSv2l6fs7OwiJ2O6ublhx44deOGFF557f7lcDpVKhdTUVPF9E1VGDNVEVcCNGzfQp08fg4Dh6OgIV1dXMTTpw01pVjNYtGgRbt26hYMHD2Lx4sVYvHgxFAoF2rVrh0GDBmH69OmF1k/W91RlZWUZNb6yqKBkrGc3f9FvNNKmTRuEhoZi6NCh4moPjx8/Fl9T0nrPz27O8fjxYzFUv/vuu7hw4QI2bdqE5cuXY/ny5ZDJZPD19cWAAQMwbdo0NG3a1OT3YaoJEybgwIEDiIiIwH//+1/xl53z58/jr7/+Es951rM9icYGIFOfUUBAAKKjowEUBOw7d+5g2bJl+Oabb/Dee+/B19dX7HF+lk6nw/jx4/Hbb7+JbTY2NnBzc4OdnR0AID09Hbm5uSavzlHe36f6daGVSmXpiyulZzd/USgUcHFxQdOmTTFgwABMmDDBYDz9382bNw/z588HUPAeL1++jIULF2L79u2YNGkSoqOj4eXl9dwaHBwcxHHvRJUVh38QVQGTJ0/GvXv34OPjg7CwMDx58gTZ2dl4/PgxHj58aDDxztieb6Bg2MOBAwdw5MgRvPfee/D394eNjQ3Onj2LTz/9FE2aNDEIPkDBrmwA8NVXX0EQhOd+6EOXKZ7d/CUhIQEXLlzAunXrMGzYsGKXTzN2975nz7O1tcXGjRtx/vx5fPLJJwgMDISjoyP++usvfPPNN2jZsiX+/e9/m/w+TBUSEgJHR0dkZWUhMjJSbNf3Unfs2FGc0Kinfz5AwfKCxjyjSZMmlblWW1tbNG7cGIsWLcK8efOQnZ2NF1980eAXHr2VK1fit99+g0KhwCeffIKbN28iLy8PKSkp4vMODQ0FULrv52eV9/epfh3u1NRUk+orjWcnZN6/fx9Xr17F1q1b8eqrr5YYqP/O0dERnTt3xpYtW9CnTx/cvHkT48aNM+prrP/rh/59E1VGDNVElVxCQgKOHTsGAPjtt98QGhpa6E/OZd0ApXv37vjXv/6FmJgYpKWlYevWrWjdujVycnIwZcoUgz/x6/+UfunSpTLd05xq1qwp/rd+rGhRnu3pL2osbNu2bbFgwQLs378faWlpiIqKQs+ePaHVasXe7Irk7Ows7taoD9JarVb8RefZdYr1nh3qINUz+vDDD9GoUSM8fvwYc+fOLXRcP6Z96tSpWLBgARo3blxomEpZv6fL+/tU//2jD5vWRC6X46effoKNjQ2io6MLzTH4u9zcXLGH2tgx5ETWiKGaqJJ7NiS2b9++yHOioqLMdj97e3sMHToUmzdvBlDwP9RnJ4v5+/sDAHbu3Gkxy2s1aNBA/EWjqE1a9PRfJ3d39xLHawMFwxH69OmDnTt3QqlUQhCEUn2d9T3hpva06umHd0RFReHhw4eIiorCgwcPYGNjgzFjxhQ6v1WrVuJY8OeFpfJia2uLjz/+GEBBr/SNGzcMjuu/p4v7fs7KysLJkyeLvb4+gJf0tS3v71P9XwhiY2PNfu2K0KRJE4wbNw4A8PHHH0Oj0RR77rPvsUWLFuVeG5FUGKqJKjmVSiX+d1E9pZmZmfjss89KfV2NRlPiigP6MZwAxHHNADBt2jTIZDKkpaXh3XffLfEearW6QoK3TCbDSy+9BABYunRpkb2ciYmJWLp0KQAUCqN5eXnFXlupVIrv/9mvw/Pog21aWprRrylK37594eXlBa1Wi19//VXssR4wYIBBD72ejY0NpkyZAgD45Zdfnrt6Rnn1tI4fPx7169eHVqvFggULDI7pv6eL6/lfuHAhMjMzi722MV/b8v4+7dmzJ4CCceumTkCU2pw5cyCXyxEbG4vVq1cXe57+F5xatWqhWbNmFVUeUYVjqCaq5Fq2bIl69eoBAKZMmWKw/Nnx48fRq1cvk8Z13rt3D02aNMFnn32GP//806Cn6uLFi+JW4E5OTmKAAIB27drhzTffBAD8/PPPGDVqFM6fPy/2Gmq1Wly4cAELFy5Eo0aNcP78+VLXZooPP/wQrq6uSElJQd++fcUhMwBw9OhR9O3bF2lpaahevTo++OADg9fWr18fc+bMwYkTJwwC9q1btzBu3Dg8ffoUcrkcQUFBRtfTqlUrAAVL35VlsqZcLhc3QVm5ciW2bNkCoOihH3pz585Fo0aNoNFoMGDAACxevNhg0mJ6ejr++OMPTJw4ET169DC5tpLY2NiIYfb333/HlStXxGMDBgwAULDN97Jly5Cfnw+gYMjH7NmzsWjRohLH7uq/tuHh4cV+75f392mLFi3EX2pK6lW3ZM2aNcPIkSMBAJ999pn4HP5O//6KmnRKVKmU3xLYRFReSrtN+fbt2wUbGxuD7bcdHR3F/46Kiip2s5HiNhh5th3/26K8evXqgp2dndhmZ2cnhIWFFapHo9EIb775psHr7e3tBXd3d4M6AQgxMTGl+toYs015caKjow224nZycjLYptzV1VU4fPhwodc9W69+i3J7e3uDbbT/85//FHpdSZuQrFu3Tny9ra2tUKdOHaF+/fqCv7+/eE5Jm78869KlSwY1qlQqIScnp8SvRWxsrLhJzrPvX78Bjv6jcePGJV6nKMZsUy4IgpCTkyN4enoKAITQ0FCxPTU1VWjevLnB1/zZbcpnzJghbpoyceLEQtc9dOiQeK5CoRBq164t1K9fv9BW4OX5fSoIgvDPf/5TACCMHTu22HPKc5vykuhfW9w25Xrnzp0Tz12yZEmh41qtVtwgZ8uWLaWug8iasKeaqAoYPHgwDh8+jEGDBsHV1RUajQYeHh6YPHkyzp07V2gNY2PUqVMH27Ztw+zZs9GtWzfUrl0bWVlZsLGxQcuWLTFr1iz89ddf4ioMz1IoFPjPf/6Dc+fOYfr06WjWrBkUCgXS09Ph5uYGf39/zJ8/H+fPnxfHtlaEgIAAXLt2DW+//TZatGgBnU4HQRDQokULvPPOO7h69WqRPbN79+7FnDlz0KNHD9StWxc5OTkAgMaNG2Py5Mk4ffq02OtprPHjx2PdunXo3r07HB0d8eDBA9y5c8ekdZdbtWplsBX2iy++CHt7+xJf06BBA5w5cwZr167F4MGDUbt2bWRnZyM/Px8NGjTAiBEjsGrVKhw/frzU9RjL3t4eb731FgAgIiJCHO7h6uqKY8eO4c0334SPjw8UCgVsbGzQq1cv/Pbbb/j5559LvG7Pnj2xc+dO9O3bFyqVCo8ePcKdO3cKrTVd3t+nM2bMAABs3brV5KX/pNa+fXsEBwcDAL744otCS+YdOnQI9+7dQ506dYrdYIaospAJQhlnwRAREZFJAgMDcfDgQfzyyy+F1gyvDKZMmYLVq1djwYIF+OSTT6Quh6hcMVQTERFJ5Pjx43jhhRfg6+uLS5cuGb1OujVISEhA48aNoVKpcOvWLUl3GCWqCBz+QUREJBE/Pz+Ehobi8uXLCAsLk7ocs/riiy+Qn5+P+fPnM1BTlcBtyomIiCT09ddfw9fXF2q1WupSzEan06FevXr47LPPMH36dKnLIaoQHP5BRERERFRGHP5BRERERFRGDNVERERERGXEUE1EREREVEYM1UREREREZcRQTURERERURgzVRERERERlxFBNRERERFRGDNVERERERGXEUE1EREREVEb/BwgfKPz9uVxYAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot ROC curve\n",
    "fig, ax = plot_roc_curve_base()\n",
    "\n",
    "# Draw ROC of individual classifier\n",
    "for i in range(len(class_list)):\n",
    "    # Make predictions and evaluate the model\n",
    "    y_test_trans = (y_test == class_list[i]).astype(int)\n",
    "    y_proba = mdl_logic_list[i].predict_proba(x_test) # Output ratio\n",
    "\n",
    "    roc_auc_logic, fpr_logic, tpr_logic, thresholds_logic = add_roc_curve(ax, y_test_trans, y_proba[:,1], color_list[i], f'{class_list[i]}')\n",
    "\n",
    "plt.legend(loc=\"lower right\", fontsize=ticklabel_size)\n",
    "plt.savefig(f'binary_roc_curve_ovr.png', dpi=300) # Make figure clearer\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "6e2942e1-671d-4589-ad1e-4220668c6d57",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 1: imgDisp label is 9, testset label is 9, predict label is 9\n",
      "Sample 2: imgDisp label is 2, testset label is 2, predict label is 0\n",
      "Sample 3: imgDisp label is 2, testset label is 2, predict label is 2\n",
      "Sample 4: imgDisp label is 9, testset label is 9, predict label is 8\n",
      "Sample 5: imgDisp label is 8, testset label is 8, predict label is 8\n",
      "Sample 6: imgDisp label is 5, testset label is 5, predict label is 5\n",
      "Sample 7: imgDisp label is 7, testset label is 7, predict label is 7\n",
      "Sample 8: imgDisp label is 7, testset label is 7, predict label is 7\n",
      "Sample 9: imgDisp label is 4, testset label is 4, predict label is 4\n",
      "Sample 10: imgDisp label is 5, testset label is 5, predict label is 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TpmjlypV6+eWX9fXXX+vGG29Uenq6li1bpsGDB2vNmjVW9/v73/9eaWlp+tvf/qa0tDQNGjRIbrdbBw4c0Nq1a7V161bvUZPevXtrx44dGjJkiHr06KGaNWvqhhtu8P4JmcIsWLBAN9xwg8aNG6d3331X7dq10+7du/U///M/io6O1oIFC8r61BVr48aNRf4M9O/fX6NGjdLw4cP1zjvvqGvXrurTp4+OHTum1atXq3fv3jpw4ECRY7ds2VIdOnTQ8OHDvddpOn78uGbNmqWWLVt69xs4cKCefPJJzZw5U3FxcRo4cKBiY2OVkZGh/fv368MPP9RTTz2ltm3bFvtYVq1aVarrNC1btkx/+MMf1KdPH7Vo0UJut1tfffWV3n//fVWrVk0LFy7UVVddVeI4QImC+dE9oKwKPv5d3HLrrbcaY366ptCsWbNM69atjdvtNldddZV55JFHTE5OTqEfMS+45MD+/fvN008/bVq2bGlq1qxpWrVqZZ599lm/a/0U+OSTT8zIkSNNTEyMqVGjhmnQoIG57rrrzNSpU82ePXv85l7W6zR98cUX5q677jJt27Y1UVFRJiQkxDRq1MjccsstZt26dYXe5oUXXjCSzMsvv2x1H0Vdp6kwRX2M/FJvv/226du3r6lbt66pUaOGadq0qUlKSjJz5871u65ORkaG+fWvf22io6NNaGio6dKli1m5cqV3XjbXaTLGmPPnz5s5c+aYTp06mbCwMBMREWHatWtnJk+ebLKysrz75eTkmHHjxpkmTZqYatWq+Tyeor5vxhhz6NAhM2bMGO81jJo0aWLGjBljDh065Ldvwcf5C1Pw2jt48GBxT6Exxve6WEUtkyZN8j6uyZMnmxYtWhi3221at25tZs6caS5cuFDoc1Ywx7Nnz5pHH33UNG3a1NSsWdO0b9/evPLKK0XO6Z///KcZMmSIiY6ONjVq1DCNGzc2119/vZk5c6bP5Qicuk7Tpk2bzB133GHi4uJM7dq1TY0aNUyzZs3MyJEjzbZt26zGAGy4jLnkDXgAld6IESOUlpamAwcOlHiFcgDATzinCaiCtm7dqkcffZRgAoBS4EgTAACABY40AQAAWCCaAAAALBBNAAAAFogmAAAACxX+4pb5+fk6evSoateuXejfsgIAACgLY4xycnIUExOjatWKPp5U4aPp6NGjQf3TAwAAoGpIT09Xs2bNitxe4d+eqyh/LR4AAFRuJTVHhY8m3pIDAADloaTmqPDRBAAAUBEENJpOnz6thx9+WDExMQoNDVWnTp301ltvBfIuAQAAAiKgJ4IPGzZM27dv1zPPPKNrrrlGS5cu1Z133qn8/HyNGjUqkHcNAADgLBMga9asMZLM0qVLfdb369fPxMTEmLy8PKtxPB6PkcTCwsLCwsLCEtDF4/EU2yQBe3tu1apVioiI0O233+6zfsyYMTp69Ki2bdsWqLsGAABwXMCi6auvvlLbtm0VEuL7DmB8fLx3OwAAwJUiYOc0ZWRkqGXLln7r69Wr591emNzcXOXm5nq/zs7ODswEAQAASiGgn54r7noHRW2bPXu2oqKivAtXAwcAABVBwKKpfv36hR5NyszMlPSfI06XmjZtmjwej3dJT08P1BQBAACsBSyaOnbsqD179igvL89n/a5duyRJHTp0KPR2brdbkZGRPgsAAECwBSyahg4dqtOnT+udd97xWb9kyRLFxMSoe/fugbprAAAAxwXsRPBBgwapX79+Gj9+vLKzsxUXF6c333xTa9eu1euvv67q1asH6q4BAAAc5zLGmEANfvr0aT3++ONatmyZMjMz1aZNG02bNk0jR460HiM7O1tRUVGBmiIAAIAkyePxFHtaUECjyQlEEwAAKA8lRVNALzkAAABQWRBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALAYumTZs2yeVyFbqkpaUF6m4BAAACIiTQd/D000+rV69ePus6dOgQ6LsFAABwVMCjqXXr1kpMTAz03QAAAAQU5zQBAABYCHg0TZgwQSEhIYqMjNSAAQO0devWQN8lAACA4wL29lxUVJQmTZqkpKQk1a9fX/v379dzzz2npKQkrVmzRgMGDCj0drm5ucrNzfV+nZ2dHagpAgAAWHMZY0x53dmpU6fUsWNH1atXT1988UWh+6SkpCg1NbW8pgQAACBJ8ng8ioyMLHJ7uUaTJI0fP14LFy7U2bNnFRYW5re9sCNNzZs3L88pAgCAKqikaAr4p+cuVdBoLper0O1ut1tut7s8pwQAAFCicv30XFZWllavXq1OnTopNDS0PO8aAACgTAJ2pGnUqFG66qqr1LVrVzVo0ED79u3T3LlzdezYMS1evDhQdwsAABAQAYum+Ph4vf3221q4cKFOnz6tevXq6YYbbtDf/vY3devWLVB3CwAAEBDlfiJ4aWVnZysqKirY0wAAAJVcSSeCc0VwAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAshwZ4AACD4wsPDHR2vQYMGjo0VHR3t2FjDhw93bKxOnTo5NlZVcfLkSUfHu+uuuxwdryQcaQIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYCAn2BADAabGxsY6O17RpU8fGCg8Pd2ysESNGODbWoEGDHBtLkpo1a+boeFXBwYMHHRvrhx9+cGysffv2OTbW/PnzHRsrGDjSBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALAQEuwJALhytWjRwrGxUlJSHBurS5cujo0lSe3bt3d0vIooNzfX0fE2btzo2FgffvihY2P97//+r2Njvf/++46NJUlnzpxxbKzz5887Nhb+gyNNAAAAFogmAAAAC0QTAACAhVJHU05OjqZMmaL+/fsrOjpaLperyHMRdu7cqb59+yoiIkJ16tTRsGHDdODAgbLOGQAAoNyVOpoyMjL00ksvKTc3V7fddluR++3du1dJSUm6cOGCli1bpkWLFumbb75Rjx49dOLEibLMGQAAoNyV+tNzsbGxysrKksvl0smTJ/XKK68Uut+MGTPkdru1evVqRUZGSvrpEy2tW7fWnDlz9Oyzz5Zt5gAAAOWo1EeaXC6XXC5Xsfvk5eVp9erVGj58uDeYpJ+Cq1evXlq1alXpZwoAABBEATkR/Ntvv9W5c+cUHx/vty0+Pl779+/nGhIAAOCKEpCLW2ZkZEiS6tWr57etXr16MsYoKytLTZo08duem5vrc5G17OzsQEwRAACgVAJ6yYHi3sYratvs2bMVFRXlXZo3bx6o6QEAAFgLSDTVr19f0n+OOP1cZmamXC6X6tSpU+htp02bJo/H413S09MDMUUAAIBSCcjbc61atVJYWJh27drlt23Xrl2Ki4tTaGhoobd1u91yu92BmBYAAMBlC8iRppCQEA0ZMkQrV65UTk6Od/2RI0e0ceNGDRs2LBB3CwAAEDCXdaTpvffe05kzZ7xBtHv3bq1YsUKSdNNNN6lWrVpKTU1Vt27ddPPNN2vq1Kk6f/68ZsyYoQYNGmjy5MnOPQIAAIBycFnRNH78eB0+fNj79fLly7V8+XJJ0sGDB9WiRQu1adNGmzZt0u9+9zuNGDFCISEh6t27t+bMmaPo6GhnZg8AAFBOLiuaDh06ZLVfly5d9MEHH1zOXQAAAFQoAb3kAAAAQGVBNAEAAFggmgAAACwE5DpNACquwv580eXatGmTY2NlZmY6NtZXX33l2FiStHTpUsfGOnv2rGNjff31146NtXHjRsfGkqSLFy86Oh5QEXCkCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGAhJNgTAFC8mJgYR8d7++23HRvLybmNHTvWsbHWr1/v2FgAUIAjTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALIcGeAFAZ1apVy7GxPv74Y8fGkqSmTZs6NtbQoUMdG2v9+vWOjQUAgcCRJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAICFkGBPAKiMVq9e7dhYzZs3d2wsSZo6dapjY7377ruOjQUAFR1HmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALIcGeAFAZLV++3LGx4uPjHRtLkh577DHHxrrpppscG2v69OmOjfWvf/3LsbEAoABHmgAAACwQTQAAABaIJgAAAAuljqacnBxNmTJF/fv3V3R0tFwul1JSUvz2Gz16tFwul9/Spk0bJ+YNAABQrkp9InhGRoZeeuklJSQk6LbbbtMrr7xS5L5hYWHasGGD3zoAAIArTamjKTY2VllZWXK5XDp58mSx0VStWjUlJiaWaYIAAAAVQamjyeVyBWIeAAAAFVpATwQ/d+6cGjdurOrVq6tZs2Z66KGHlJmZGci7BAAACIiAXdwyISFBCQkJ6tChgyRp8+bNmjdvntavX6/t27crIiKi0Nvl5uYqNzfX+3V2dnagpggAAGAtYNH029/+1ufrfv36qXPnzhoxYoRefvllv+0FZs+erdTU1EBNCwAA4LKU63Wahg4dqvDwcKWlpRW5z7Rp0+TxeLxLenp6Oc4QAACgcOX+t+eMMapWrehWc7vdcrvd5TgjAACAkpXrkaYVK1bo7NmzXIYAAABccS7rSNN7772nM2fOKCcnR5K0e/durVixQtJPf/X8xIkTGjVqlEaOHKm4uDi5XC5t3rxZ8+fPV/v27XXfffc59wgAAADKwWVF0/jx43X48GHv18uXL9fy5cslSQcPHlRUVJQaNWqk559/XseOHdPFixcVGxuriRMnavr06QoPD3dm9gAAAOXksqLp0KFDJe6zcuXKyxkaAACgQirXc5oAAACuVEQTAACABZcxxgR7EsXJzs5WVFRUsKcBBE3dunUdHW/SpEmOjTV58mTHxrp48aJjY3Xt2tWxsSRp//79jo4HoGLyeDyKjIwscjtHmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWQoI9AaCiCAsLc2ys0NBQx8bKyspybCxJSklJcWysixcvOjZWamqqY2O98MILjo0lSYMHD3Z0PABXJo40AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACyEBHsCQFnMnDnTsbFGjx7t2Fhut9uxsbZt2+bYWJL0xz/+0bGx/v73vzs2VmpqqmNjnTx50rGxAKAAR5oAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAACyHBngBQFgMGDHBsrKZNmzo2lpMGDx5cYcf79NNPHRvLSSEh/NMGwHkcaQIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYCAn2BICyWLJkiWNjde3a1bGxnORyuRwdzxjj2FhdunRxbKwLFy44Ntbrr7/u2FgAUIAjTQAAABaIJgAAAAtEEwAAgIVSRdOGDRt07733qk2bNgoPD1fTpk1166236tNPP/Xbd+fOnerbt68iIiJUp04dDRs2TAcOHHBs4gAAAOWpVNG0YMECHTp0SJMmTdI//vEPvfDCCzp+/LgSExO1YcMG73579+5VUlKSLly4oGXLlmnRokX65ptv1KNHD504ccLxBwEAABBopfr03F/+8hc1bNjQZ93AgQMVFxenp59+Wr1795YkzZgxQ263W6tXr1ZkZKSknz5l07p1a82ZM0fPPvusQ9MHAAAoH6U60nRpMElSRESE2rVrp/T0dElSXl6eVq9ereHDh3uDSZJiY2PVq1cvrVq1qoxTBgAAKH9lPhHc4/Fo586dat++vSTp22+/1blz5xQfH++3b3x8vPbv36/z58+X9W4BAADKVZkvbjlhwgSdOXNGjz/+uCQpIyNDklSvXj2/fevVqydjjLKystSkSZNCx8vNzVVubq736+zs7LJOEQAAoMzKdKTpySef1BtvvKF58+b5XRm4uKsYF7dt9uzZioqK8i7NmzcvyxQBAAAccdnRlJqaqqeeekqzZs3SQw895F1fv359Sf854vRzmZmZcrlcqlOnTpHjTps2TR6Px7sUnCsFAAAQTJf19lxqaqpSUlKUkpKi6dOn+2xr1aqVwsLCtGvXLr/b7dq1S3FxcQoNDS1ybLfbLbfbfTnTAgAACJhSH2maOXOmUlJS9MQTTyg5Odlve0hIiIYMGaKVK1cqJyfHu/7IkSPauHGjhg0bVrYZAwAABEGpjjTNnTtXM2bM0MCBAzV48GClpaX5bE9MTJT005Gobt266eabb9bUqVN1/vx5zZgxQw0aNNDkyZOdmz0AAEA5KVU0vfvuu5KktWvXau3atX7bjTGSpDZt2mjTpk363e9+pxEjRigkJES9e/fWnDlzFB0d7cC0AQAAylepomnTpk3W+3bp0kUffPBBaecDAABQIZX54pYAAABVAdEEAABgocxXBAeCacmSJY6NVdz1w0rrl7/8pWNjOS0rK8uxsb755hvHxnr55ZcdG+vo0aOOjQUABTjSBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALDgMsaYYE+iONnZ2YqKigr2NAAAQCXn8XgUGRlZ5HaONAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACAhVJF04YNG3TvvfeqTZs2Cg8PV9OmTXXrrbfq008/9dlv9OjRcrlcfkubNm0cnTwAAEB5CSnNzgsWLFBGRoYmTZqkdu3a6cSJE5o7d64SExO1bt069e7d27tvWFiYNmzY4HP7sLAwZ2YNAABQzlzGGGO78/Hjx9WwYUOfdadPn1ZcXJw6dOigDz74QNJPR5pWrFih06dPl3mC2dnZioqKKvM4AAAAxfF4PIqMjCxye6nenrs0mCQpIiJC7dq1U3p6eulnBwAAcIUo84ngHo9HO3fuVPv27X3Wnzt3To0bN1b16tXVrFkzPfTQQ8rMzCzr3QEAAARFqc5pKsyECRN05swZPf744951CQkJSkhIUIcOHSRJmzdv1rx587R+/Xpt375dERERRY6Xm5ur3Nxc79fZ2dllnSIAAEDZmTJ44oknjCTzpz/9qcR9V6xYYSSZ559/vtj9kpOTjSQWFhYWFhYWlnJdPB5PsY1y2dGUkpJiJJlZs2ZZ7X/x4kUTHh5u7rjjjmL3O3/+vPF4PN4lPT096E8iCwsLCwsLS+VfSoqmy3p7LjU1VSkpKUpJSdH06dOtb2eMUbVqxZ9G5Xa75Xa7L2daAAAAAVPqE8FnzpyplJQUPfHEE0pOTra+3YoVK3T27FklJiaW9i4BAACCrlRHmubOnasZM2Zo4MCBGjx4sNLS0ny2JyYm6vDhwxo1apRGjhypuLg4uVwubd68WfPnz1f79u113333OfoAAAAAykOpLm6ZlJSkzZs3F7ndGKOsrCyNHTtWn332mY4dO6aLFy8qNjZWQ4cO1fTp00t9oUoubgkAAMpDSRe3LFU0BQPRBAAAyoOjVwQHAACoqogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACwQTQAAABaIJgAAAAtEEwAAgAWiCQAAwALRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABYIJoAAAAsEE0AAAAWiCYAAAALRBMAAIAFogkAAMAC0QQAAGCBaAIAALBANAEAAFggmgAAACxU+GgyxgR7CgAAoAooqTkqfDTl5OQEewoAAKAKKKk5XKaCH8rJz8/X0aNHVbt2bblcriL3y87OVvPmzZWenq7IyMhynCEknv9g4/kPLp7/4ON7EFxX+vNvjFFOTo5iYmJUrVrRx5NCynFOl6VatWpq1qyZ9f6RkZFX5DessuD5Dy6e/+Di+Q8+vgfBdSU//1FRUSXuU+HfngMAAKgIiCYAAAALlSaa3G63kpOT5Xa7gz2VKonnP7h4/oOL5z/4+B4EV1V5/iv8ieAAAAAVQaU50gQAABBIRBMAAIAFogkAAMDCFR1Np0+f1sMPP6yYmBiFhoaqU6dOeuutt4I9rSpj06ZNcrlchS5paWnBnl6lkpOToylTpqh///6Kjo6Wy+VSSkpKofvu3LlTffv2VUREhOrUqaNhw4bpwIED5TvhSsj2ezB69OhCfybatGlT/pOuJDZs2KB7771Xbdq0UXh4uJo2bapbb71Vn376qd++vP6dZ/v8V4XXfoW/uGVxhg0bpu3bt+uZZ57RNddco6VLl+rOO+9Ufn6+Ro0aFezpVRlPP/20evXq5bOuQ4cOQZpN5ZSRkaGXXnpJCQkJuu222/TKK68Uut/evXuVlJSkTp06admyZTp//rxmzJihHj166PPPP1d0dHQ5z7zysP0eSFJYWJg2bNjgtw6XZ8GCBcrIyNCkSZPUrl07nThxQnPnzlViYqLWrVun3r17S+L1Hyi2z79UBV775gq1Zs0aI8ksXbrUZ32/fv1MTEyMycvLC9LMqo6NGzcaSWb58uXBnkqll5+fb/Lz840xxpw4ccJIMsnJyX773X777aZBgwbG4/F41x06dMjUqFHDTJkypbymWynZfg/uueceEx4eXs6zq9yOHTvmty4nJ8c0atTI9OnTx7uO139g2D7/VeG1f8W+Pbdq1SpFRETo9ttv91k/ZswYHT16VNu2bQvSzADnFRzmLk5eXp5Wr16t4cOH+/wZg9jYWPXq1UurVq0K9DQrNZvvAQKjYcOGfusiIiLUrl07paenS+L1H0g2z39VccVG01dffaW2bdsqJMT3Hcb4+HjvdpSPCRMmKCQkRJGRkRowYIC2bt0a7ClVSd9++63OnTvn/Rn4ufj4eO3fv1/nz58PwsyqnnPnzqlx48aqXr26mjVrpoceekiZmZnBnlal4vF4tHPnTrVv314Sr//ydunzX6Cyv/av2HOaMjIy1LJlS7/19erV825HYEVFRWnSpElKSkpS/fr1tX//fj333HNKSkrSmjVrNGDAgGBPsUopeM0X/Az8XL169WSMUVZWlpo0aVLeU6tSEhISlJCQ4D2vb/PmzZo3b57Wr1+v7du3KyIiIsgzrBwmTJigM2fO6PHHH5fE67+8Xfr8S1XjtX/FRpOkYg+Vcxg98Dp37qzOnTt7v+7Ro4eGDh2qjh07asqUKURTkPBzEVy//e1vfb7u16+fOnfurBEjRujll1/2247Se/LJJ/XGG2/oT3/6k7p06eKzjdd/4BX1/FeF1/4V+/Zc/fr1Cz2aVHAYsLD/bSDw6tSpo5tvvllffvmlzp07F+zpVCn169eXVPhR1szMTLlcLtWpU6ecZwVJGjp0qMLDw7kUhwNSU1P11FNPadasWXrooYe863n9l4+inv+iVLbX/hUbTR07dtSePXuUl5fns37Xrl2S+Mh7MJn//3OG/K+ufLVq1UphYWHen4Gf27Vrl+Li4hQaGhqEmUH66eeiWrUr9p/cCiE1NVUpKSlKSUnR9OnTfbbx+g+84p7/4lSm1/4V+yiGDh2q06dP65133vFZv2TJEsXExKh79+5BmlnVlpWVpdWrV6tTp078A1XOQkJCNGTIEK1cuVI5OTne9UeOHNHGjRs1bNiwIM6ualuxYoXOnj2rxMTEYE/lijVz5kylpKToiSeeUHJyst92Xv+BVdLzX5TK9tq/Ys9pGjRokPr166fx48crOztbcXFxevPNN7V27Vq9/vrrql69erCnWOmNGjVKV111lbp27aoGDRpo3759mjt3ro4dO6bFixcHe3qVznvvvaczZ854fyHs3r1bK1askCTddNNNqlWrllJTU9WtWzfdfPPNmjp1qvfifg0aNNDkyZODOf1KoaTvwYkTJzRq1CiNHDlScXFxcrlc2rx5s+bPn6/27dvrvvvuC+b0r1hz587VjBkzNHDgQA0ePNjvrZ6CX8i8/gPD5vk/fPhw1XjtB/UqUWWUk5NjJk6caBo3bmxq1qxp4uPjzZtvvhnsaVUZs2fPNp06dTJRUVGmevXqJjo62gwdOtR88sknwZ5apRQbG2skFbocPHjQu9+OHTtMnz59TK1atUxkZKS57bbbzP79+4M38UqkpO9BZmamGTp0qGnRooUJCwszNWvWNK1btzZTpkwxp06dCvb0r1g9e/Ys8nm/9NcYr3/n2Tz/VeW17zLm/09AAQAAQJGu2HOaAAAAyhPRBAAAYIFoAgAAsEA0AQAAWCCaAAAALBBNAAAAFogmAAAAC0QTAACABaIJAADAAtEEAABggWgCAACwQDQBAABY+D/44/7DlA3xhAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_num = 10\n",
    "\n",
    "# Random select 3 examples from imgDisp and testset\n",
    "np.random.seed(1)\n",
    "idx = np.random.choice(len(imgDisp), sample_num)\n",
    "\n",
    "# Select instances\n",
    "imgDisp_select = [imgDisp[i] for i in idx]\n",
    "testset_select = [testset[i] for i in idx]\n",
    "\n",
    "# Check the selected instances' labels are the same\n",
    "for i in range(sample_num):\n",
    "    x = testset_select[i][0].view(-1, input_size)\n",
    "\n",
    "    # Using model to predict character\n",
    "    y_pred_list = []\n",
    "    for j in range(len(mdl_logic_list)):\n",
    "        y_pred_list.append(mdl_logic_list[j].predict(x))\n",
    "\n",
    "    y_pred = np.argmax(np.array(y_pred_list), axis=0)[0]\n",
    "\n",
    "    # Display image from imgDisp\n",
    "    fig, ax = plt.subplots(figsize=(7,7))\n",
    "    ax.imshow(imgDisp_select[i][0], cmap='gray')\n",
    "    ax.tick_params(axis='both', which='major', labelsize=ticklabel_size) # Set tick label size\n",
    "    ax.set_title(f\"Label: {imgDisp_select[i][1]}, Prediction Label: {y_pred}\", fontsize=label_size)\n",
    "\n",
    "    print(f'Sample {i+1}: imgDisp label is {imgDisp_select[i][1]}, testset label is {testset_select[i][1]}, predict label is {y_pred}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "86f407be-6ed9-4ffb-bf06-c32add952f16",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7572\n"
     ]
    }
   ],
   "source": [
    "# Prediction\n",
    "y_pred_list = []\n",
    "for i in range(len(mdl_logic_list)):\n",
    "    y_pred_list.append(mdl_logic_list[i].predict(x_test))\n",
    "\n",
    "y_pred = np.argmax(np.array(y_pred_list), axis=0)\n",
    "\n",
    "# Accuracy\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "print(f'Accuracy: {accuracy:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfad7dd7-24d1-4fce-a369-043bc7b570ee",
   "metadata": {},
   "source": [
    "### 一对一（One-vs-One）方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "bddcae3e-147a-4835-badd-99c3e7b46055",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 3.85 seconds\n",
      "Accuracy: 0.8776\n"
     ]
    }
   ],
   "source": [
    "# Define logic regression classifier\n",
    "mdl_logic_ovo = OneVsOneClassifier(LogisticRegression(max_iter=1000))\n",
    "\n",
    "# Train model\n",
    "start_time = time.time()\n",
    "mdl_logic_ovo.fit(x_train, y_train)\n",
    "end_time = time.time()\n",
    "\n",
    "print(f'Training time: {end_time - start_time:.2f} seconds')\n",
    "\n",
    "# Make predictions and evaluate the model\n",
    "y_pred = mdl_logic_ovo.predict(x_test)\n",
    "\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "print(f'Accuracy: {accuracy:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "edf86989-85f4-499d-95dd-49fcc3fe40b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training class 0 (5923) vs class 1 (6742), Training time: 0.08 seconds, Precision: 0.9918, Recall (Sensitivity): 0.9918, Specificity: 0.9930, Accuracy: 0.9924, F1-Score: 0.9918\n",
      "Training class 0 (5923) vs class 2 (5958), Training time: 0.13 seconds, Precision: 0.9828, Recall (Sensitivity): 0.9939, Specificity: 0.9835, Accuracy: 0.9886, F1-Score: 0.9883\n",
      "Training class 0 (5923) vs class 3 (6131), Training time: 0.05 seconds, Precision: 0.9929, Recall (Sensitivity): 0.9939, Specificity: 0.9931, Accuracy: 0.9935, F1-Score: 0.9934\n",
      "Training class 0 (5923) vs class 4 (5842), Training time: 0.05 seconds, Precision: 0.9959, Recall (Sensitivity): 0.9898, Specificity: 0.9959, Accuracy: 0.9929, F1-Score: 0.9928\n",
      "Training class 0 (5923) vs class 5 (5421), Training time: 0.06 seconds, Precision: 0.9698, Recall (Sensitivity): 0.9837, Specificity: 0.9664, Accuracy: 0.9754, F1-Score: 0.9767\n",
      "Training class 0 (5923) vs class 6 (5918), Training time: 0.06 seconds, Precision: 0.9847, Recall (Sensitivity): 0.9878, Specificity: 0.9843, Accuracy: 0.9861, F1-Score: 0.9862\n",
      "Training class 0 (5923) vs class 7 (6265), Training time: 0.05 seconds, Precision: 0.9828, Recall (Sensitivity): 0.9918, Specificity: 0.9835, Accuracy: 0.9875, F1-Score: 0.9873\n",
      "Training class 0 (5923) vs class 8 (5851), Training time: 0.11 seconds, Precision: 0.9776, Recall (Sensitivity): 0.9806, Specificity: 0.9774, Accuracy: 0.9790, F1-Score: 0.9791\n",
      "Training class 0 (5923) vs class 9 (5949), Training time: 0.08 seconds, Precision: 0.9798, Recall (Sensitivity): 0.9908, Specificity: 0.9802, Accuracy: 0.9854, F1-Score: 0.9853\n",
      "Training class 1 (6742) vs class 0 (5923), Training time: 0.06 seconds, Precision: 0.9930, Recall (Sensitivity): 0.9930, Specificity: 0.9918, Accuracy: 0.9924, F1-Score: 0.9930\n",
      "Training class 1 (6742) vs class 2 (5958), Training time: 0.06 seconds, Precision: 0.9860, Recall (Sensitivity): 0.9930, Specificity: 0.9845, Accuracy: 0.9889, F1-Score: 0.9895\n",
      "Training class 1 (6742) vs class 3 (6131), Training time: 0.06 seconds, Precision: 0.9672, Recall (Sensitivity): 0.9885, Specificity: 0.9624, Accuracy: 0.9762, F1-Score: 0.9778\n",
      "Training class 1 (6742) vs class 4 (5842), Training time: 0.06 seconds, Precision: 0.9982, Recall (Sensitivity): 0.9956, Specificity: 0.9980, Accuracy: 0.9967, F1-Score: 0.9969\n",
      "Training class 1 (6742) vs class 5 (5421), Training time: 0.06 seconds, Precision: 0.9817, Recall (Sensitivity): 0.9938, Specificity: 0.9765, Accuracy: 0.9862, F1-Score: 0.9877\n",
      "Training class 1 (6742) vs class 6 (5918), Training time: 0.06 seconds, Precision: 0.9843, Recall (Sensitivity): 0.9930, Specificity: 0.9812, Accuracy: 0.9876, F1-Score: 0.9886\n",
      "Training class 1 (6742) vs class 7 (6265), Training time: 0.05 seconds, Precision: 0.9742, Recall (Sensitivity): 0.9991, Specificity: 0.9708, Accuracy: 0.9857, F1-Score: 0.9865\n",
      "Training class 1 (6742) vs class 8 (5851), Training time: 0.06 seconds, Precision: 0.9735, Recall (Sensitivity): 0.9700, Specificity: 0.9692, Accuracy: 0.9697, F1-Score: 0.9718\n",
      "Training class 1 (6742) vs class 9 (5949), Training time: 0.05 seconds, Precision: 0.9852, Recall (Sensitivity): 0.9991, Specificity: 0.9832, Accuracy: 0.9916, F1-Score: 0.9921\n",
      "Training class 2 (5958) vs class 0 (5923), Training time: 0.10 seconds, Precision: 0.9941, Recall (Sensitivity): 0.9835, Specificity: 0.9939, Accuracy: 0.9886, F1-Score: 0.9888\n",
      "Training class 2 (5958) vs class 1 (6742), Training time: 0.06 seconds, Precision: 0.9922, Recall (Sensitivity): 0.9845, Specificity: 0.9930, Accuracy: 0.9889, F1-Score: 0.9883\n",
      "Training class 2 (5958) vs class 3 (6131), Training time: 0.08 seconds, Precision: 0.9518, Recall (Sensitivity): 0.9380, Specificity: 0.9515, Accuracy: 0.9447, F1-Score: 0.9449\n",
      "Training class 2 (5958) vs class 4 (5842), Training time: 0.05 seconds, Precision: 0.9941, Recall (Sensitivity): 0.9855, Specificity: 0.9939, Accuracy: 0.9896, F1-Score: 0.9898\n",
      "Training class 2 (5958) vs class 5 (5421), Training time: 0.06 seconds, Precision: 0.9236, Recall (Sensitivity): 0.9138, Specificity: 0.9126, Accuracy: 0.9132, F1-Score: 0.9187\n",
      "Training class 2 (5958) vs class 6 (5918), Training time: 0.09 seconds, Precision: 0.9613, Recall (Sensitivity): 0.9632, Specificity: 0.9582, Accuracy: 0.9608, F1-Score: 0.9622\n",
      "Training class 2 (5958) vs class 7 (6265), Training time: 0.03 seconds, Precision: 0.9779, Recall (Sensitivity): 0.9845, Specificity: 0.9776, Accuracy: 0.9811, F1-Score: 0.9812\n",
      "Training class 2 (5958) vs class 8 (5851), Training time: 0.06 seconds, Precision: 0.9880, Recall (Sensitivity): 0.9574, Specificity: 0.9877, Accuracy: 0.9721, F1-Score: 0.9724\n",
      "Training class 2 (5958) vs class 9 (5949), Training time: 0.05 seconds, Precision: 0.9836, Recall (Sensitivity): 0.9893, Specificity: 0.9832, Accuracy: 0.9863, F1-Score: 0.9865\n",
      "Training class 3 (6131) vs class 0 (5923), Training time: 0.06 seconds, Precision: 0.9941, Recall (Sensitivity): 0.9931, Specificity: 0.9939, Accuracy: 0.9935, F1-Score: 0.9936\n",
      "Training class 3 (6131) vs class 1 (6742), Training time: 0.06 seconds, Precision: 0.9868, Recall (Sensitivity): 0.9624, Specificity: 0.9885, Accuracy: 0.9762, F1-Score: 0.9744\n",
      "Training class 3 (6131) vs class 2 (5958), Training time: 0.06 seconds, Precision: 0.9376, Recall (Sensitivity): 0.9515, Specificity: 0.9380, Accuracy: 0.9447, F1-Score: 0.9445\n",
      "Training class 3 (6131) vs class 4 (5842), Training time: 0.06 seconds, Precision: 1.0000, Recall (Sensitivity): 0.9891, Specificity: 1.0000, Accuracy: 0.9945, F1-Score: 0.9945\n",
      "Training class 3 (6131) vs class 5 (5421), Training time: 0.06 seconds, Precision: 0.8754, Recall (Sensitivity): 0.9248, Specificity: 0.8509, Accuracy: 0.8901, F1-Score: 0.8994\n",
      "Training class 3 (6131) vs class 6 (5918), Training time: 0.06 seconds, Precision: 0.9911, Recall (Sensitivity): 0.9911, Specificity: 0.9906, Accuracy: 0.9909, F1-Score: 0.9911\n",
      "Training class 3 (6131) vs class 7 (6265), Training time: 0.10 seconds, Precision: 0.9641, Recall (Sensitivity): 0.9564, Specificity: 0.9650, Accuracy: 0.9607, F1-Score: 0.9602\n",
      "Training class 3 (6131) vs class 8 (5851), Training time: 0.11 seconds, Precision: 0.9602, Recall (Sensitivity): 0.9564, Specificity: 0.9589, Accuracy: 0.9577, F1-Score: 0.9583\n",
      "Training class 3 (6131) vs class 9 (5949), Training time: 0.05 seconds, Precision: 0.9704, Recall (Sensitivity): 0.9743, Specificity: 0.9703, Accuracy: 0.9723, F1-Score: 0.9723\n",
      "Training class 4 (5842) vs class 0 (5923), Training time: 0.05 seconds, Precision: 0.9899, Recall (Sensitivity): 0.9959, Specificity: 0.9898, Accuracy: 0.9929, F1-Score: 0.9929\n",
      "Training class 4 (5842) vs class 1 (6742), Training time: 0.08 seconds, Precision: 0.9949, Recall (Sensitivity): 0.9980, Specificity: 0.9956, Accuracy: 0.9967, F1-Score: 0.9964\n",
      "Training class 4 (5842) vs class 2 (5958), Training time: 0.04 seconds, Precision: 0.9849, Recall (Sensitivity): 0.9939, Specificity: 0.9855, Accuracy: 0.9896, F1-Score: 0.9894\n",
      "Training class 4 (5842) vs class 3 (6131), Training time: 0.06 seconds, Precision: 0.9889, Recall (Sensitivity): 1.0000, Specificity: 0.9891, Accuracy: 0.9945, F1-Score: 0.9944\n",
      "Training class 4 (5842) vs class 5 (5421), Training time: 0.05 seconds, Precision: 0.9799, Recall (Sensitivity): 0.9919, Specificity: 0.9776, Accuracy: 0.9851, F1-Score: 0.9858\n",
      "Training class 4 (5842) vs class 6 (5918), Training time: 0.05 seconds, Precision: 0.9858, Recall (Sensitivity): 0.9898, Specificity: 0.9854, Accuracy: 0.9876, F1-Score: 0.9878\n",
      "Training class 4 (5842) vs class 7 (6265), Training time: 0.06 seconds, Precision: 0.9770, Recall (Sensitivity): 0.9939, Specificity: 0.9776, Accuracy: 0.9856, F1-Score: 0.9854\n",
      "Training class 4 (5842) vs class 8 (5851), Training time: 0.06 seconds, Precision: 0.9859, Recall (Sensitivity): 0.9949, Specificity: 0.9856, Accuracy: 0.9903, F1-Score: 0.9904\n",
      "Training class 4 (5842) vs class 9 (5949), Training time: 0.09 seconds, Precision: 0.9398, Recall (Sensitivity): 0.9532, Specificity: 0.9405, Accuracy: 0.9468, F1-Score: 0.9464\n",
      "Training class 5 (5421) vs class 0 (5923), Training time: 0.05 seconds, Precision: 0.9818, Recall (Sensitivity): 0.9664, Specificity: 0.9837, Accuracy: 0.9754, F1-Score: 0.9740\n",
      "Training class 5 (5421) vs class 1 (6742), Training time: 0.06 seconds, Precision: 0.9920, Recall (Sensitivity): 0.9765, Specificity: 0.9938, Accuracy: 0.9862, F1-Score: 0.9842\n",
      "Training class 5 (5421) vs class 2 (5958), Training time: 0.06 seconds, Precision: 0.9014, Recall (Sensitivity): 0.9126, Specificity: 0.9138, Accuracy: 0.9132, F1-Score: 0.9070\n",
      "Training class 5 (5421) vs class 3 (6131), Training time: 0.08 seconds, Precision: 0.9090, Recall (Sensitivity): 0.8509, Specificity: 0.9248, Accuracy: 0.8901, F1-Score: 0.8790\n",
      "Training class 5 (5421) vs class 4 (5842), Training time: 0.06 seconds, Precision: 0.9909, Recall (Sensitivity): 0.9776, Specificity: 0.9919, Accuracy: 0.9851, F1-Score: 0.9842\n",
      "Training class 5 (5421) vs class 6 (5918), Training time: 0.06 seconds, Precision: 0.9788, Recall (Sensitivity): 0.9821, Specificity: 0.9802, Accuracy: 0.9811, F1-Score: 0.9804\n",
      "Training class 5 (5421) vs class 7 (6265), Training time: 0.08 seconds, Precision: 0.9618, Recall (Sensitivity): 0.9585, Specificity: 0.9669, Accuracy: 0.9630, F1-Score: 0.9601\n",
      "Training class 5 (5421) vs class 8 (5851), Training time: 0.09 seconds, Precision: 0.9448, Recall (Sensitivity): 0.9025, Specificity: 0.9517, Accuracy: 0.9282, F1-Score: 0.9232\n",
      "Training class 5 (5421) vs class 9 (5949), Training time: 0.05 seconds, Precision: 0.9633, Recall (Sensitivity): 0.9720, Specificity: 0.9673, Accuracy: 0.9695, F1-Score: 0.9676\n",
      "Training class 6 (5918) vs class 0 (5923), Training time: 0.05 seconds, Precision: 0.9874, Recall (Sensitivity): 0.9843, Specificity: 0.9878, Accuracy: 0.9861, F1-Score: 0.9859\n",
      "Training class 6 (5918) vs class 1 (6742), Training time: 0.06 seconds, Precision: 0.9916, Recall (Sensitivity): 0.9812, Specificity: 0.9930, Accuracy: 0.9876, F1-Score: 0.9864\n",
      "Training class 6 (5918) vs class 2 (5958), Training time: 0.11 seconds, Precision: 0.9603, Recall (Sensitivity): 0.9582, Specificity: 0.9632, Accuracy: 0.9608, F1-Score: 0.9592\n",
      "Training class 6 (5918) vs class 3 (6131), Training time: 0.08 seconds, Precision: 0.9906, Recall (Sensitivity): 0.9906, Specificity: 0.9911, Accuracy: 0.9909, F1-Score: 0.9906\n",
      "Training class 6 (5918) vs class 4 (5842), Training time: 0.07 seconds, Precision: 0.9895, Recall (Sensitivity): 0.9854, Specificity: 0.9898, Accuracy: 0.9876, F1-Score: 0.9874\n",
      "Training class 6 (5918) vs class 5 (5421), Training time: 0.08 seconds, Precision: 0.9832, Recall (Sensitivity): 0.9802, Specificity: 0.9821, Accuracy: 0.9811, F1-Score: 0.9817\n",
      "Training class 6 (5918) vs class 7 (6265), Training time: 0.05 seconds, Precision: 0.9969, Recall (Sensitivity): 0.9969, Specificity: 0.9971, Accuracy: 0.9970, F1-Score: 0.9969\n",
      "Training class 6 (5918) vs class 8 (5851), Training time: 0.09 seconds, Precision: 0.9801, Recall (Sensitivity): 0.9749, Specificity: 0.9805, Accuracy: 0.9777, F1-Score: 0.9775\n",
      "Training class 6 (5918) vs class 9 (5949), Training time: 0.05 seconds, Precision: 0.9948, Recall (Sensitivity): 0.9969, Specificity: 0.9950, Accuracy: 0.9959, F1-Score: 0.9958\n",
      "Training class 7 (6265) vs class 0 (5923), Training time: 0.06 seconds, Precision: 0.9921, Recall (Sensitivity): 0.9835, Specificity: 0.9918, Accuracy: 0.9875, F1-Score: 0.9878\n",
      "Training class 7 (6265) vs class 1 (6742), Training time: 0.05 seconds, Precision: 0.9990, Recall (Sensitivity): 0.9708, Specificity: 0.9991, Accuracy: 0.9857, F1-Score: 0.9847\n",
      "Training class 7 (6265) vs class 2 (5958), Training time: 0.03 seconds, Precision: 0.9843, Recall (Sensitivity): 0.9776, Specificity: 0.9845, Accuracy: 0.9811, F1-Score: 0.9810\n",
      "Training class 7 (6265) vs class 3 (6131), Training time: 0.08 seconds, Precision: 0.9575, Recall (Sensitivity): 0.9650, Specificity: 0.9564, Accuracy: 0.9607, F1-Score: 0.9612\n",
      "Training class 7 (6265) vs class 4 (5842), Training time: 0.08 seconds, Precision: 0.9941, Recall (Sensitivity): 0.9776, Specificity: 0.9939, Accuracy: 0.9856, F1-Score: 0.9858\n",
      "Training class 7 (6265) vs class 5 (5421), Training time: 0.08 seconds, Precision: 0.9641, Recall (Sensitivity): 0.9669, Specificity: 0.9585, Accuracy: 0.9630, F1-Score: 0.9655\n",
      "Training class 7 (6265) vs class 6 (5918), Training time: 0.06 seconds, Precision: 0.9971, Recall (Sensitivity): 0.9971, Specificity: 0.9969, Accuracy: 0.9970, F1-Score: 0.9971\n",
      "Training class 7 (6265) vs class 8 (5851), Training time: 0.08 seconds, Precision: 0.9698, Recall (Sensitivity): 0.9669, Specificity: 0.9682, Accuracy: 0.9675, F1-Score: 0.9683\n",
      "Training class 7 (6265) vs class 9 (5949), Training time: 0.14 seconds, Precision: 0.9676, Recall (Sensitivity): 0.9300, Specificity: 0.9683, Accuracy: 0.9489, F1-Score: 0.9484\n",
      "Training class 8 (5851) vs class 0 (5923), Training time: 0.11 seconds, Precision: 0.9804, Recall (Sensitivity): 0.9774, Specificity: 0.9806, Accuracy: 0.9790, F1-Score: 0.9789\n",
      "Training class 8 (5851) vs class 1 (6742), Training time: 0.08 seconds, Precision: 0.9652, Recall (Sensitivity): 0.9692, Specificity: 0.9700, Accuracy: 0.9697, F1-Score: 0.9672\n",
      "Training class 8 (5851) vs class 2 (5958), Training time: 0.10 seconds, Precision: 0.9563, Recall (Sensitivity): 0.9877, Specificity: 0.9574, Accuracy: 0.9721, F1-Score: 0.9717\n",
      "Training class 8 (5851) vs class 3 (6131), Training time: 0.12 seconds, Precision: 0.9550, Recall (Sensitivity): 0.9589, Specificity: 0.9564, Accuracy: 0.9577, F1-Score: 0.9570\n",
      "Training class 8 (5851) vs class 4 (5842), Training time: 0.08 seconds, Precision: 0.9948, Recall (Sensitivity): 0.9856, Specificity: 0.9949, Accuracy: 0.9903, F1-Score: 0.9902\n",
      "Training class 8 (5851) vs class 5 (5421), Training time: 0.10 seconds, Precision: 0.9133, Recall (Sensitivity): 0.9517, Specificity: 0.9013, Accuracy: 0.9277, F1-Score: 0.9321\n",
      "Training class 8 (5851) vs class 6 (5918), Training time: 0.08 seconds, Precision: 0.9755, Recall (Sensitivity): 0.9805, Specificity: 0.9749, Accuracy: 0.9777, F1-Score: 0.9780\n",
      "Training class 8 (5851) vs class 7 (6265), Training time: 0.09 seconds, Precision: 0.9652, Recall (Sensitivity): 0.9682, Specificity: 0.9669, Accuracy: 0.9675, F1-Score: 0.9667\n",
      "Training class 8 (5851) vs class 9 (5949), Training time: 0.09 seconds, Precision: 0.9613, Recall (Sensitivity): 0.9702, Specificity: 0.9623, Accuracy: 0.9662, F1-Score: 0.9658\n",
      "Training class 9 (5949) vs class 0 (5923), Training time: 0.08 seconds, Precision: 0.9910, Recall (Sensitivity): 0.9802, Specificity: 0.9908, Accuracy: 0.9854, F1-Score: 0.9856\n",
      "Training class 9 (5949) vs class 1 (6742), Training time: 0.06 seconds, Precision: 0.9990, Recall (Sensitivity): 0.9832, Specificity: 0.9991, Accuracy: 0.9916, F1-Score: 0.9910\n",
      "Training class 9 (5949) vs class 2 (5958), Training time: 0.08 seconds, Precision: 0.9890, Recall (Sensitivity): 0.9832, Specificity: 0.9893, Accuracy: 0.9863, F1-Score: 0.9861\n",
      "Training class 9 (5949) vs class 3 (6131), Training time: 0.06 seconds, Precision: 0.9741, Recall (Sensitivity): 0.9703, Specificity: 0.9743, Accuracy: 0.9723, F1-Score: 0.9722\n",
      "Training class 9 (5949) vs class 4 (5842), Training time: 0.13 seconds, Precision: 0.9538, Recall (Sensitivity): 0.9405, Specificity: 0.9532, Accuracy: 0.9468, F1-Score: 0.9471\n",
      "Training class 9 (5949) vs class 5 (5421), Training time: 0.06 seconds, Precision: 0.9750, Recall (Sensitivity): 0.9673, Specificity: 0.9720, Accuracy: 0.9695, F1-Score: 0.9711\n",
      "Training class 9 (5949) vs class 6 (5918), Training time: 0.05 seconds, Precision: 0.9970, Recall (Sensitivity): 0.9950, Specificity: 0.9969, Accuracy: 0.9959, F1-Score: 0.9960\n",
      "Training class 9 (5949) vs class 7 (6265), Training time: 0.13 seconds, Precision: 0.9314, Recall (Sensitivity): 0.9683, Specificity: 0.9300, Accuracy: 0.9489, F1-Score: 0.9495\n",
      "Training class 9 (5949) vs class 8 (5851), Training time: 0.09 seconds, Precision: 0.9710, Recall (Sensitivity): 0.9623, Specificity: 0.9702, Accuracy: 0.9662, F1-Score: 0.9667\n"
     ]
    }
   ],
   "source": [
    "def get_scores(tp, fp, tn, fn):\n",
    "    precision = tp / (tp + fp)\n",
    "    recall = tp / (tp + fn) # Also called sensitivity\n",
    "    accuracy = (tp + tn) / (tp + fp + tn + fn)\n",
    "    f1 = 2 * precision * recall / (precision + recall)\n",
    "\n",
    "    specificity = tn / (tn + fp)\n",
    "\n",
    "    return precision, recall, specificity, accuracy, f1\n",
    "# Get class list: 0, 1, ..., 9\n",
    "class_list = np.sort(np.unique(y_train))\n",
    "\n",
    "# Create model matrix to save models\n",
    "mdl_logic_matrix = {}\n",
    "for cls_p in class_list:\n",
    "    mdl_logic_matrix[cls_p] = {}\n",
    "    for cls_n in class_list:\n",
    "        if cls_p == cls_n:\n",
    "            continue\n",
    "        mdl_logic_matrix[cls_p][cls_n] = LogisticRegression(max_iter=1000)\n",
    "\n",
    "for cls_p in class_list:\n",
    "    # Training data of positive class\n",
    "    x_train_ovo_p = x_train[(y_train == cls_p), :]\n",
    "    y_train_ovo_p = np.ones(x_train_ovo_p.shape[0])\n",
    "\n",
    "    # Testing data of positive class\n",
    "    x_test_ovo_p = x_test[(y_test == cls_p), :]\n",
    "    y_test_ovo_p = np.ones(x_test_ovo_p.shape[0])\n",
    "\n",
    "    for cls_n in class_list:\n",
    "        if cls_p == cls_n:\n",
    "            continue\n",
    "\n",
    "        # Training data of negative class\n",
    "        x_train_ovo_n = x_train[(y_train == cls_n), :]\n",
    "        y_train_ovo_n = np.zeros(x_train_ovo_n.shape[0])\n",
    "\n",
    "        # Testing data of negative class\n",
    "        x_test_ovo_n = x_test[(y_test == cls_n), :]\n",
    "        y_test_ovo_n = np.zeros(x_test_ovo_n.shape[0])\n",
    "\n",
    "        # Concatenate data for training\n",
    "        x_train_ovo = np.concatenate((x_train_ovo_p, x_train_ovo_n), axis=0)\n",
    "        y_train_ovo = np.concatenate((y_train_ovo_p, y_train_ovo_n), axis=0)\n",
    "\n",
    "        # Model training\n",
    "        start_time = time.time()\n",
    "        mdl_logic_matrix[cls_p][cls_n].fit(x_train_ovo, y_train_ovo)\n",
    "        end_time = time.time()\n",
    "\n",
    "        # Concatenate data for testing\n",
    "        x_test_ovo = np.concatenate((x_test_ovo_p, x_test_ovo_n), axis=0)\n",
    "        y_test_ovo = np.concatenate((y_test_ovo_p, y_test_ovo_n), axis=0)\n",
    "\n",
    "        # Test model on sub-task\n",
    "        y_proba_ovo = mdl_logic_matrix[cls_p][cls_n].predict_proba(x_test_ovo) # Output ratio\n",
    "\n",
    "        # Display results\n",
    "        _, (tp, fp, tn, fn) = cls_counts(y_test_ovo, y_proba_ovo[:, 1])\n",
    "        precision, recall, specificity, accuracy, f1 = get_scores(tp, fp, tn, fn)\n",
    "        print(f'Training class {cls_p} ({x_train_ovo_p.shape[0]}) vs class {cls_n} ({x_train_ovo_n.shape[0]}), Training time: {end_time - start_time:.2f} seconds, Precision: {precision:.4f}, Recall (Sensitivity): {recall:.4f}, Specificity: {specificity:.4f}, Accuracy: {accuracy:.4f}, F1-Score: {f1:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbf0af70-a5e9-444a-ba87-8c7e736e2898",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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